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THIS IS A MAPLE BUG SAMPLE

 BUG # 1 int: INVALID INDEFINITE INTEGRATION
 Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
 Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
 Maple 9.00, IBM INTEL NT, Jun 13 2003 Build ID 136194
 Maple 8.01, IBM INTEL NT, May  1 2002 Build ID 119670

 EXAMPLE 1:      int(sin(z)*exp(z)*sin(1/z), z);

 ACTUAL:         0

 EXPECTED:       int(sin(z)*exp(z)*sin(1/z), z);


 EXAMPLE 2:      diff(int(sin(z)*exp(z)*cos(1/z), z),z);

 ACTUAL:         exp(z)*sin(z)

 EXPECTED:       sin(z)*exp(z)*cos(1/z)


 The same problem with

 int(sin(z)*exp(-z)*sin(1/z), z);
 int(cos(z)*exp(z)*sin(1/z), z);
 int(cos(z)*exp(-z)*sin(1/z), z);
 diff(int(exp(z)*cos(z+1/z), z), z);
 diff(int(exp(z)*cos(z-1/z), z), z);
 diff(int(exp(-z)*cos(z+1/z), z), z);
 diff(int(exp(-z)*cos(z-1/z), z), z);


2003-2004 Cyber Tester, LLC


All rights reserved. All logos and trademarks are property of their respective owners.














Dear Mr. Cooper,

Maple bug analysis is going to be the death of me. You know that I have already thereby forfeited one eye, and from that I was in some considerable danger. One morning, while I was bent over to examine a portion of a novelty, a Maple bug genetic map which was sent to me by one of our promising computer scientists, I suddenly felt a blow of pain. This work, in which one must hang over and examine a large area at one time, attacks the sight far more violently than only simple reading or writing alone. On account of these things, I must ask you, if you have good will for me, to appeal to Mr. Bernardin if it would please him that I be excused from this work, which is only a small part of my responsibilities, but which easily make me unfit for all the rest. I am with all honor and respect your humble servant,

Leonhard Euler



HOT NEWS:     MAPLE 9  BUG  LISTS ARE  COMING  SOON


Maplesoft, Inc.announces the upcoming release of Maple 9 between late June and late July 2003.

The Cyber Tester, LLC announces Maple 9 extensive bug lists will be published within 30 days after we get access to Maple 9.



Produced by our GEMM, below is published for the first time a tiny random demo of Maple howlers in 10 functions:

limit, int, sum, product, simplify, series, asympt, coulditbe, is, testeq.



BUG # 1         int: INVALID INDEFINITE INTEGRATION
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      int(sin(z)*exp(z)*sin(1/z), z);

ACTUAL:         0

EXPECTED:       int(sin(z)*exp(z)*sin(1/z), z);


EXAMPLE 2:      diff(int(sin(z)*exp(z)*cos(1/z), z),z);

ACTUAL:         exp(z)*sin(z)

EXPECTED:       sin(z)*exp(z)*cos(1/z)


The same problem with

int(sin(z)*exp(-z)*sin(1/z), z);
int(cos(z)*exp(z)*sin(1/z), z);
int(cos(z)*exp(-z)*sin(1/z), z);
diff(int(exp(z)*cos(z+1/z), z), z);
diff(int(exp(z)*cos(z-1/z), z), z);
diff(int(exp(-z)*cos(z+1/z), z), z);
diff(int(exp(-z)*cos(z-1/z), z), z);

BUG # 2         int: INVALID INDEFINITE INTEGRATION
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                int(sqrt(sqrt(z)-1),z);

ACTUAL:         -I/Pi^(1/2)*(-8/15*Pi^(1/2)-4/15*Pi^(1/2)*(-1+z^(1/2))*(3*z^(1/2)+2)*(1-z^(1/2\
                ))^(1/2))

HINT:           func := sqrt(sqrt(z)-1): simplify(func-diff(int(func,z),z)); plot(%, z=0..2);

                ((z^(1/2)-1)^(1/2)*(1-z^(1/2))^(1/2)*z^(1/2)-I*z^(1/2)+I*z)/(1-z^(1/2))^(1/2)/\
                z^(1/2)

                while the above expression should be equal to 0 identically.

EXPECTED:       4/15*(z^(1/2)-1)^(1/2)*(-2-z^(1/2)+3*z)

CHECKUP:        simplify(sqrt(sqrt(z)-1)-diff(4/15*(z^(1/2)-1)^(1/2)*(-2-z^(1/2)+3*z),z));

                0

CHECKUP:        plot(func-diff(4/15*(z^(1/2)-1)^(1/2)*(-2-z^(1/2)+3*z),z),z=-10..10,y=-1..1);
                plot(func-diff(4/15*(z^(1/2)-1)^(1/2)*(-2-z^(1/2)+3*z),z),z=-999..999,y=-1..1);


IMPLICATIONS:   Maple calculates incorrectly definite integrals involving  sqrt(sqrt(z)-1)


EXAMPLE 1:      INVALID OUTPUT SIGN:

                evalf(int(sqrt(sqrt(z)-1), z=1..2));

ACTUAL:         -.4437859441

EXPECTED:       .4437859441

CHECKUP:        evalf(Int(sqrt(sqrt(z)-1), z=1..2));

                .4437859441


EXAMPLE 2:      INVALID MAGNITUDE OF THE REALS AND IMAGINARY PARTS

                evalf(int(sqrt(sqrt(I*z)-1), z=-1..1));

ACTUAL:         1.591279201*I

EXPECTED:       .6108037585

CHECKUP:        evalf(Int(sqrt(sqrt(I*z)-1), z=-1..1));

                .6108037585

BUG # 3         int: INVALID MAGNITUDE OF THE REAL-VALUED INTEGRAL
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                int(exp(-z^2)/(1+z^2), z=1..infinity);

ACTUAL:         1/2*Pi*exp(1)-1/2*Pi*exp(1)*erf(1)

                .671646711

EXPECTED:       1/2*Pi*exp(1)-1/2*Pi*exp(1)*erf(1)-sum(1/2*(-1)^n*(2/(n+1/2)/(3+2*n)*exp(-1/2)\
                *WhittakerM(1/2*n+1/4,1/2*n+3/4,1)+1/(n+1/2)*exp(-1/2)*WhittakerM(1/2*n+5/4,1/\
                2*n+3/4,1)),n = 0 .. infinity)

                .528247477e-1

CHECKUP:        evalf(Int(exp(-z^2)/(1+z^2), z=1..infinity));

                .5282474752e-1

The same problem with

int(exp(-z^(3/2))/(1+z^(3/2)), z=1..infinity);
int(exp(-z^(2/3))/(1+z^(2/3)), z=1..infinity);
int(exp(-z^(4/3))/(1+z^(4/3)), z=1..infinity);
int(exp(-z^(3/4))/(1+z^(3/4)), z=1..infinity);
int(exp(-z^3)/(1+z^3), z=1..infinity);
int(exp(-z^4)/(1+z^4), z=1..infinity);
int(exp(-z^5)/(1+z^5), z=1..infinity);
int(exp(-z^6)/(1+z^6), z=1..infinity);
int(Ei(0, 1+z^2), z=1..infinity);
int(Ei(0, 1+z^3), z=1..infinity);
int(Ei(0, 1+z^4), z=1..infinity);
int(Ei(0, 1+z^5), z=1..infinity);

BUG # 4         int: Error, (in limit/range) should not happen 33
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                int(arctan(tan(1/z)), z=0..1);

ACTUAL:         Error, (in limit/range) should not happen 33

The same problem with

int(ln(z)*arctan(tan(1/z)), z=0..1);
int(sqrt(z)*arctan(tan(1/z)), z=0..1);
int(z^(1/3)*arctan(tan(1/z)), z=0..1);
int(exp(-z)*arctan(tan(z)), z=0..infinity);
int(exp(-z^2)*arctan(tan(z)), z=0..infinity);
int(exp(-z^3)*arctan(tan(z)), z=0..infinity);
int(exp(-2*z)*arctan(tan(z))*cosh(z), z=0..infinity);

BUG # 5         int: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      int(arcsec(z*sqrt(1 - z^2)), z = -2..2);

ACTUAL:         undefined

EXPECTED:       2*Pi

WORKAROUND:     subs(a=2,int(arcsec(z*sqrt(1 - z^2)), z = -a..a));


EXAMPLE 2:      int(arccsc(z*sqrt(1 - z^2)), z = -2..2);

ACTUAL:         undefined

EXPECTED:       0

WORKAROUND:     subs(a=2,int(arccsc(z*sqrt(1 - z^2)), z = -a..a));


COMMENT:        Derive 5.06 calculates all these integrals correctly.

The same problem with

int(arcsec(z*sqrt(1 + z^2)), z = -2..2);
int(arccsc(z*sqrt(1 + z^2)), z = -2..2);
int(arccsc(z*sqrt(1 - z^2)), z = -2..2);
int(arccsch(z*sqrt(1 - z^2)), z = -2..2);

BUG # 6         int: INVALID INDEFINITE INTEGRATION
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                int(arctan(tan(1/z)), z);

ACTUAL:         z*arctan(tan(1/z))+ln(z)

EXPECTED:       -Pi*z*floor(1/(Pi*z)+1/2)+Psi(floor(1/(Pi*z)+1/2)+1/2)+ln(z)

CHECKUP:        evalf(subs(z=1, %)-subs(z=1/20, %),15);
                evalf(Int(arctan(tan(1/z)), z=1/20..1),14);

                .18178871320958
                .18178871320958

The same problem with

int(arctan(cot(1/z)), z);
int(arccot(cot(1/z)), z);
int(arccot(tan(1/z)), z);

BUG # 7         sum: INVALID MAGNITUDE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                evalf(sum(sin(Pi/2^n),  n=1..infinity));

ACTUAL:         1

EXPECTED:       2.481049919

CHECKUP:        evalf(Sum(sin(Pi/2^n),  n=1..infinity));

                2.481049919

HINT:           plot(sum(sin(Pi/2^n),  n=1..k), k=1..100);

The same problem with

sum((-1)^n*sin(Pi/2^n),  n=1..infinity);
sum(sin(Pi/3^n),  n=1..infinity);
sum(sin(Pi/4^n),  n=2..infinity);
sum((-1)^n*sin(Pi/3^n),  n=1..infinity);
sum((-1)^n*sin(Pi/4^n),  n=2..infinity);
sum(n^2*sin(Pi/(3^n))^2, n=1..infinity);
sum(4^n*sin(Pi/(5^n)), n=1..infinity);

BUG # 8         int: Error, (in X) numeric exception: division by zero
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                int(arctan(z*sqrt(1 - z^2)), z = -2..2);

ACTUAL:         Error, (in ln) numeric exception: division by zero

EXPECTED:       0

CHECKUP:        evalf(Int(arctan(z*sqrt(1 - z^2)), z = -2..2, method = _CCquad));

                0.+0.*I

HINT:           plot(Re(arctan(z*sqrt(1 - z^2))), z = -2..2);
                plot(Im(arctan(z*sqrt(1 - z^2))), z = -2..2);

COMMENT:        Derive 5.06 calculates this integral correctly.

COMMENT:        Maple cannot see that the integrand is an odd bounded function;
                thus, the integral of it over any finite symmetric segment is
                equal to zero.

BUG # 9         limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(arcsin(1/cos(z)),z = Pi/2-4);

ACTUAL:         undefined

EXPECTED:       arcsin(1/sin(4))

                -1.570796327+.7816340727*I

CHECKUP:        evalf(Limit(arcsin(1/cos(z)),z = Pi/2-4));

                -1.570796327+.7816340724*I

COMMENT:        Derive 5.06 and Mathematica 4.2.1 calculate all these limits correctly.

The same problem with

limit(arcsin(1/cos(z)),z = Pi/2-5);
limit(arccos(1/cos(z)),z = Pi/2-4);
limit(arccos(1/cos(z)),z = Pi/2-5);
limit(arcsin(1/cos(z)),z = 5-Pi/2);
limit(arccos(1/cos(z)),z = 4-Pi/2);
limit(arccos(1/cos(z)),z = 5-Pi/2);
limit(arcsin(1/cos(z)),z = 5+Pi/2);
limit(arccos(1/cos(z)),z = 4+Pi/2);
limit(arccos(1/cos(z)),z = 5+Pi/2);
limit(arcsin(1/cos(z)),z = 111+Pi/2);
limit(arccos(1/cos(z)),z = 111+Pi/2);

BUG # 10        limit: BEYOND CLASSIFICATION
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(sin(z)^2+cos(z)^2, z = infinity);

ACTUAL:         0 .. 2

EXPECTED:       1

CHECKUP:        seq(round(evalf(limit(sin(z)^2+cos(z)^2, z = 10^k))), k=1..20);

                1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

WORKAROUND:     limit(simplify(sin(z)^2+cos(z)^2), z = infinity);

COMMENT:        Derive 5.06 and MuPAD 2.5.2 calculate it correctly.
::::::::::::::::::::::::::::::::::::::::::::::::: 10%

BUG # 11        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(sqrt(1-ln(1+1/z^2)), z=1);

ACTUAL:         undefined

EXPECTED:       (1-ln(2))^(1/2)

                .5539429749

CHECKUP:        evalf(Limit(sqrt(1-ln(1+1/z^2)), z=1));

                .5539429749


EXAMPLE 2:      limit(sqrt(1-ln(1+1/z^2)), z=1, left);

ACTUAL:         -(1-ln(2))^(1/2)

EXPECTED:       (1-ln(2))^(1/2)

                .5539429749

CHECKUP:        evalf(Limit(sqrt(1-ln(1+1/z^2)), z=1-1/10^100));

                .5539429749

HINT:           plot(sqrt(1-ln(1+1/z^2)), z=1..3);
                plot(sqrt(1-ln(1+1/z^2)), z=9/10..11/10);

BUG # 12        limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(sin(1/sqrt(z))*z,z = 0);

ACTUAL:         0

EXPECTED:       undefined

CHECKUP:        evalf(limit(sin(1/sqrt(z))*z,z = -1/10^10));
                evalf(limit(sin(1/sqrt(z))*z,z = 1/10^10));

                .1403331680e43420*I
                .3574879797e-11

EXAMPLE 2:      limit(sin(1/z)*z,z = 0,left);

ACTUAL:         0

EXPECTED:       I*infinity

CHECKUP:        evalf(limit(sin(1/sqrt(z))*z,z = -1/10^10));

                .1403331680e43420*I

COMMENT:        Derive 5.06 and Mathematica 4.2.1 calculate these limits correctly.

BUG # 13        limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(sqrt(-sinh(z)), z = Pi/2+1, left);

ACTUAL:         -1/2*I*2^(1/2)*(-1/exp(Pi)^(1/2)*exp(-1)+exp(Pi)^(1/2)*exp(1))^(1/2)

                -2.549486088*I

EXPECTED:       1/2*I*2^(1/2)*(-exp(-1)+exp(Pi+1))^(1/2)*exp(-1/4*Pi)

                2.549486087*I

CHECKUP:        evalf(Limit(sqrt(-sinh(z)), z = Pi/2+1, left));

                2.549486088*I


EXAMPLE 2:      limit(sqrt(-sinh(z)), z = Pi/2+1, right);

ACTUAL:         -1/2*I*2^(1/2)*(-1/exp(Pi)^(1/2)*exp(-1)+exp(Pi)^(1/2)*exp(1))^(1/2)

                -2.549486088*I

EXPECTED:       1/2*I*2^(1/2)*(-exp(-1)+exp(1+Pi))^(1/2)*exp(-1/4*Pi)

                2.549486087*I

CHECKUP:        evalf(Limit(sqrt(-sinh(z)), z = Pi/2+1, right));

                2.549486088*I

COMMENT:        Derive 5.06 and Mathematica 4.2.1 calculate these limits
                correctly.

BUG # 14        limit: HISTORY-DEPENDENT OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`

The results of the INDEPENDENT computations depend on the previous inputs; in other words,
the outcomes of the INDEPENDENT computations are not the same for the  a;b;  and  the b;a;
sequences.

                limit((csch(z)^2-1)^(1/3),z = 1);
                limit((csch(z)^2-1)^(1/3),z = 11);
                restart;
                limit((csch(z)^2-1)^(1/3),z = 11);
                limit((csch(z)^2-1)^(1/3),z = 1);

ACTUAL:         1/2*(-6/(exp(1)-exp(-1))^2+1/(exp(1)-exp(-1))^2*exp(-2)+1/(exp(\
                1)-exp(-1))^2*exp(2))^(1/3)+1/2*I*(-6/(exp(1)-exp(-1))^2+1/(exp\
                (1)-exp(-1))^2*exp(-2)+1/(exp(1)-exp(-1))^2*exp(2))^(1/3)*3^(1/\
                2)
                1/2*(-6/(exp(11)-exp(-11))^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/\
                (exp(11)-exp(-11))^2*exp(22))^(1/3)+1/2*I*(-6/(exp(11)-exp(-11)\
                )^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/(exp(11)-exp(-11))^2*exp(\
                22))^(1/3)*3^(1/2)
                undefined
                undefined

EXPECTED:       1/2*(-6/(exp(1)-exp(-1))^2+1/(exp(1)-exp(-1))^2*exp(-2)+1/(exp(\
                1)-exp(-1))^2*exp(2))^(1/3)+1/2*I*(-6/(exp(1)-exp(-1))^2+1/(exp\
                (1)-exp(-1))^2*exp(-2)+1/(exp(1)-exp(-1))^2*exp(2))^(1/3)*3^(1/\
                2)
                1/2*(-6/(exp(11)-exp(-11))^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/\
                (exp(11)-exp(-11))^2*exp(22))^(1/3)+1/2*I*(-6/(exp(11)-exp(-11)\
                )^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/(exp(11)-exp(-11))^2*exp(\
                22))^(1/3)*3^(1/2)
                1/2*(-6/(exp(1)-exp(-1))^2+1/(exp(1)-exp(-1))^2*exp(-2)+1/(exp(\
                1)-exp(-1))^2*exp(2))^(1/3)+1/2*I*(-6/(exp(1)-exp(-1))^2+1/(exp\
                (1)-exp(-1))^2*exp(-2)+1/(exp(1)-exp(-1))^2*exp(2))^(1/3)*3^(1/\
                2)
                1/2*(-6/(exp(11)-exp(-11))^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/\
                (exp(11)-exp(-11))^2*exp(22))^(1/3)+1/2*I*(-6/(exp(11)-exp(-11)\
                )^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/(exp(11)-exp(-11))^2*exp(\
                22))^(1/3)*3^(1/2)

BUG # 15        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                restart;
                limit((csch(z)^2-1)^(1/3),z = 11);

ACTUAL:         undefined

EXPECTED:       (1/sinh(11)^2*(sinh(11)^2 - 1))^(1/3)*(1/2*I*3^(1/2) + 1/2)

                .4999999998+.8660254037*I

CHECKUP:        evalf(Limit((csch(z)^2-1)^(1/3),z = 11));

                .4999999998+.8660254035*I

BUG # 16        evalf: INVALID MAGNITUDE OF THE REAL AND IMAGINARY PARTS
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`

1) The values of approximations are not correct.
2) What is even worse, Maple is NOT consistent with itself. Compare with Mathematica.

                restart;
                func := EllipticF(I,2*I):
                evalf(evalf(func,  10), 10);
                evalf(evalf(func,  20), 10);
                evalf(evalf(func, 100), 10);

ACTUAL:         .5328240547+.7423732236*I      #   <---------------------------------.
                .5604418122+.7421443374*I      #   <-- These values must be identical.
                .5499902134+.7397678082*I      #   <---------------------------------.

EXPECTED:       .5499964467+.7422062367*I
                .5499964467+.7422062367*I
                .5499964467+.7422062367*I

COMMENT:        Mathematica 4.2.1 approximates these inputs correctly.

                N[N[EllipticF[ArcSin[I], -4], 10], 10]
                N[N[EllipticF[ArcSin[I], -4], 20], 10]
                N[N[EllipticF[ArcSin[I], -4], 100], 10]

                0.549996 + 0.742206 I
                0.549996 + 0.742206 I
                0.549996 + 0.742206 I

BUG # 17        limit: INVALID TYPE OF DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


This is like  2 + 2 = sin(z).


                limit(cos(sqrt(-z)),z = infinity);

ACTUAL:         -1 .. 1

EXPECTED:       infinity

CHECKUP:        seq(evalf(limit(cos(sqrt(-z)),z = 10^k)), k=15..20);

                .1198972659e13733598,
                .7749883733e43429448,
                .3143132997e137335974,
                .4001490885e434294482,
                .4818341088e1373359738,
                Float(infinity)

The same problem with

limit(sin(sqrt(-z)), z = infinity);
limit(cos(sqrt(-z))+sin(z),z = infinity);
limit(cos(sqrt(-z))+cos(z),z = infinity);
limit(sin(sqrt(-z))+sin(z),z = infinity);
limit(sin(sqrt(-z))+cos(z),z = infinity);

COMMENT:        Mathematica 4.2.1 calculates all these limits correctly.
                Derive 5.06 does 4 first of them, too.

BUG # 18        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(tan(z)*cot(z),z = infinity);

ACTUAL:         undefined

EXPECTED:       1

CHECKUP:        evalf(Limit(tan(z)*cot(z),z = infinity));

                1.000000000

The same problem with

limit(tan(z)*cot(z),z = -infinity);

COMMENT:        Derive 5.06, Mathematica 4.2.1 and MuPAD 2.5.2 calculate
                it correctly.

                LIM(COT(z)*TAN(z), z, inf)

                1

                Limit[Tan[z]*Cot[z], z -> Infinity]

                1

                limit(cot(z)*tan(z),z = infinity);

                1

BUG # 19        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit((1/z-(1-1/z^2))^(1/3),z = 2);

ACTUAL:         undefined

EXPECTED:       1/4*2^(1/3)+1/4*I*2^(1/3)*3^(1/2)

                .3149802625+.5455618182*I

CHECKUP:        evalf(Limit((1/z-(1-1/z^2))^(1/3),z = 2));

                .3149802625+.5455618180*I


EXAMPLE 2:      limit((1/z-(1-1/z^2))^(1/3),z = 2, left);

ACTUAL:         1/8*4^(2/3)-1/8*I*4^(2/3)*3^(1/2)

EXPECTED:       1/8*4^(2/3)+1/8*I*4^(2/3)*3^(1/2)

                .3149802625+.5455618181*I

CHECKUP:        evalf(Limit((1/z-(1-1/z^2))^(1/3),z = 1.999999999));

                .3149802623+.5455618176*I

COMMENT:        Derive 5.06 and Mathematica 4.2.1 calculate these limits
                correctly.

The same problem with

limit((1/z-(1+1/z^2))^(1/3),z = 2);
limit((1/z^2-(1-1/z^2))^(1/3),z = 2);
limit((1/z^4-(1-1/z^2))^(1/3),z = 2);
limit((1/z^4-(1-1/z^3))^(1/3),z = 2);
limit((1/z^4-(1-1/z^4))^(1/3),z = 2);
limit((1/z^4-(1-1/z^4))^(1/3),z = 2);
limit(1/(1/z^4-(1-1/z^4))^(1/3),z = 2);
limit(1/(1/z^4-(1-1/z^4)^(1/1))^(1/3),z = 2);
limit(1/(1/z^4-(1-1/z^4)^(1/2))^(1/3),z = 2);
limit(1/(-1/z^4-(1-1/z^4)^(1/2))^(1/3),z = 2);
limit((1/z-(1+1/z^2))^(1/3),z = 2, left);
limit((1/z^2-(1-1/z^2))^(1/3),z = 2, left);
limit((1/z^4-(1-1/z^2))^(1/3),z = 2, left);
limit((1/z^4-(1-1/z^3))^(1/3),z = 2, left);
limit((1/z^4-(1-1/z^4))^(1/3),z = 2, left);
limit((1/z^4-(1-1/z^4))^(1/3),z = 2, left);
limit(1/(1/z^4-(1-1/z^4))^(1/3),z = 2, left);
limit(1/(1/z^4-(1-1/z^4)^(1/1))^(1/3),z = 2, left);
limit(1/(1/z^4-(1-1/z^4)^(1/2))^(1/3),z = 2, left);
limit(1/(-1/z^4-(1-1/z^4)^(1/2))^(1/3),z = 2, left);

BUG # 20        limit: Error, (in X) should not happen 33
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(arctan(tan(z)),z = infinity);

ACTUAL:         Error, (in limit/range) should not happen 33

EXPECTED:       -Pi/2..Pi/2

HINT:           plot(arctan(tan(z)),z = 1000..1020);

COMMENT:        Mathematica 4.2.1 calculates it correctly.

The same problem with

limit(arccot(tan(z)),z = infinity);
limit(arctanh(tan(z)),z = infinity);
::::::::::::::::::::::::::::::::::::::::::::::::: 20%

BUG # 21        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit((ln(z)/(1+z^3)^2-1)^(1/3),z = 2);

ACTUAL:         undefined

EXPECTED:       1/18*(-ln(2)+162)^(1/3)*(3^(2/3)+3*I*3^(1/6))

                .6290607728+1.089565219*I

CHECKUP:        evalf(Limit((ln(z)^2/(1+z^3)^2-2)^(1/3),z = 2));

                .6290607726+1.089565219*I

EXAMPLE 2:      limit((ln(z)/(1+z^3)^2-1)^(1/3),z = 2, left);

ACTUAL:         1/162*81^(2/3)*(-ln(2)+81)^(1/3)-1/162*I*81^(2/3)*(-ln(2)+81)\
                ^(1/3)*3^(1/2)

                .4985696836-.8635480234*I

EXPECTED:       1/162*81^(2/3)*(-ln(2)+81)^(1/3)+1/162*I*81^(2/3)*(-ln(2)+81)\
                ^(1/3)*3^(1/2)

                .4985696836+.8635480234*I

CHECKUP:        evalf(Limit((ln(z)/(1+z^3)^2-1)^(1/3),z = 2));

                .4985696835+.8635480230*I

The same problem with

limit((ln(z)/(1+z^3)^2-2)^(1/3),z = 2);
limit((ln(z)^2/(1+z^3)^2-2)^(1/3),z = 2);
limit((ln(z)^2/(1+z^3)^2-2)^(1/4),z = 2);
limit((ln(z)^2/(1+z^3)^2-2)^(1/4),z = 10);
limit((ln(z)/(1+z^3)^2-2)^(1/3),z = 2, left);
limit((ln(z)^2/(1+z^3)^2-2)^(1/3),z = 2, left);
limit((ln(z)^2/(1+z^3)^2-2)^(1/4),z = 2, left);
limit((ln(z)^2/(1+z^3)^2-2)^(1/4),z = 10, left);

BUG # 22        limit: INVALID MAGNITUDE OF THE REAL-VALUED LIMIT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(Fresnelf(z),z = -infinity);

ACTUAL:         0

EXPECTED:       1

CHECKUP:        evalf(limit(Fresnelf(z),z = -10^10));

                1.000000000

EXAMPLE 2:      limit(Fresnelg(z),z = -infinity);

ACTUAL:         0

EXPECTED:       1

CHECKUP:        evalf(Limit(Fresnelg(z),z = -infinity));

                1.000000000

BUG # 23        limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(arccot(1/sqrt(z)),z = -infinity);

ACTUAL:         -1/2*Pi

EXPECTED:       1/2*Pi

                1.570796327

CHECKUP:        fnormal(evalf(Limit(arccot(1/sqrt(z)),z = -infinity)));

                1.570796327+0.*I

BUG # 24        limit: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(BesselJ(0, sqrt(z)),z = -infinity);

ACTUAL:         0

EXPECTED:       infinity

CHECKUP:        seq(evalf(Limit(BesselJ(0, sqrt(z)),z = -10^k)), k=8..10);

                .3513456066e4341, .8877534180e13731, .3540796227e43427


EXAMPLE 2:      limit(BesselJ(1, sqrt(z)),z = -infinity);

ACTUAL:         0

EXPECTED:       I*infinity

CHECKUP:        seq(evalf(Limit(BesselJ(1, sqrt(z)),z = -10^k)), k=8..10);

                .3513280389e4341*I, .8877393813e13731*I, .3540778523e43427*I

BUG # 25        limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(arctanh(sqrt(z))*BesselK(0,z),z = -infinity);

ACTUAL:         0

EXPECTED:       infinity

CHECKUP:        evalf(limit(arctanh(sqrt(z))*BesselK(0,z),z = -10^5));
                evalf(limit(arctanh(sqrt(z))*BesselK(0,z),z = -10^10));

                .1743795279e43428
                Float(infinity)

BUG # 26        limit: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                evalf(Limit(sqrt(z)*EllipticPi(1/2,z), z= infinity));

ACTUAL:         Float(infinity)

EXPECTED:       0

CHECKUP:        evalf(Limit(sqrt(z)*EllipticPi(1/2,z), z= 1000000000000));
                .1570796327e-5-.2980271364e-4*I

                evalf(Limit(sqrt(z)*EllipticPi(1/2,z), z= 10^20), 50);

                .15707963267948966192313216916397514420986632395039e-9-
                .48223394384398252608809954182423513009224676425905e-8*I

BUG # 27        limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(KelvinKei(0,z),z = -infinity);

ACTUAL:         0

EXPECTED:       undefined

CHECKUP:        seq(evalf(limit(KelvinKei(0,z),z = -10^k)), k=5..9);

                -.4518269280e30707+0.*I,
                .6756894672e307089+0.*I,
                .1853952270e3070923+0.*I,
                -.1675955604e30709254+0.*I,
                .2220299636e307092569+0.*I

The same problem with

limit(KelvinKer(0,z),z = -infinity);
limit(KelvinKer(1,z),z = -infinity);
limit(KelvinKer(2,z),z = -infinity);
limit(KelvinKer(3,z),z = -infinity);
limit(KelvinKer(4,z),z = -infinity);

limit(KelvinKei(1,z),z = -infinity);
limit(KelvinKei(2,z),z = -infinity);
limit(KelvinKei(3,z),z = -infinity);
limit(KelvinKei(4,z),z = -infinity);

limit(KelvinBer(0,z),z = -infinity);
limit(KelvinBer(1,z),z = -infinity);
limit(KelvinBer(2,z),z = -infinity);
limit(KelvinBer(3,z),z = -infinity);
limit(KelvinBer(4,z),z = -infinity);

limit(KelvinBei(0,z),z = -infinity);
limit(KelvinBei(1,z),z = -infinity);
limit(KelvinBei(2,z),z = -infinity);
limit(KelvinBei(3,z),z = -infinity);
limit(KelvinBei(4,z),z = -infinity);

limit(KelvinHer(0,z),z = -infinity);
limit(KelvinHer(1,z),z = -infinity);
limit(KelvinHer(2,z),z = -infinity);
limit(KelvinHer(3,z),z = -infinity);
limit(KelvinHer(4,z),z = -infinity);

limit(KelvinHei(0,z),z = -infinity);
limit(KelvinHei(1,z),z = -infinity);
limit(KelvinHei(2,z),z = -infinity);
limit(KelvinHei(3,z),z = -infinity);
limit(KelvinHei(4,z),z = -infinity);

limit(KelvinKer(0,z),z = -infinity);
limit(KelvinKei(0,z),z = -infinity);
limit(KelvinBer(0,z),z = -infinity);
limit(KelvinBei(0,z),z = -infinity);

limit(ln(z)*KelvinHer(0,z),z = -infinity);
limit(ln(z)*KelvinHei(0,z),z = -infinity);
limit(KelvinKei(2,z)*HankelH1(1/3,z),z = -infinity);
limit(arccot(z)-KelvinKei(0,z),z = -infinity);
limit(Chi(z)-KelvinKer(1,z),z = -infinity);

BUG # 28        limit: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(EllipticPi(1,z),z = 0);

ACTUAL:         Error, (in depends/internal) too many levels of recursion

EXPECTED:       limit(EllipticPi(1,z),z = 0)   or  complex_infinity

BUG # 29        evalf: MEANINGLESS OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                evalf(EllipticPi(1,0));

ACTUAL:         answer

EXPECTED:       EllipticPi(1,0)

BUG # 30        limit: MEANINGLESS OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(z/BesselY(0,I*sqrt(z)),z = infinity);

ACTUAL:         signum(O(1))*infinity

EXPECTED:       0

CHECKUP:        evalf(Limit(z/BesselY(0,I*sqrt(z)),z = 10^19));

                -.4854522468e-1373359757-.1236050411e-1373359713*I

int(polylog(2,1-I/z^(3/2)),z = 1..infinity);
int(polylog(2,1+I/z^(3/2)),z = 1..infinity);
int(polylog(2,1+1/z^(3/2)),z = 1..infinity);
int(polylog(2,1-1/z^(3/2)),z = 1..infinity);
int(polylog(2,1-I/z^(3/2)),z = 2..infinity);
int(polylog(2,1+I/z^(3/2)),z = 2..infinity);
int(polylog(2,1-1/z^(3/2)),z = 2..infinity);
int(polylog(2,1+1/z^(3/2)),z = 2..infinity);
::::::::::::::::::::::::::::::::::::::::::::::::: 30%

BUG # 31        limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(arccoth(1/(1-sqrt(1-z))),z = infinity);

ACTUAL:         1/2*I*Pi

                1.570796327*I

EXPECTED:       -1/2*I*Pi

CHECKUP:        fnormal(evalf(limit(arccoth(1/(1-sqrt(1-z))),z = 10^(10^2)),30));

                0.-1.570796327*I

The same problem with

limit(arccoth(1/ln(z-sqrt(1-z))),z = infinity);
limit(arccoth(1/tanh(z^(1/3)-(1-z^(1/3))^(1/2))),z = infinity);
limit(arccoth(1/cosh(z^(1/4)-(1-z^(1/5))^(1/9))),z = infinity);

BUG # 32        limit: INVALID MAGNITUDE OF THE IMAGINARY PART
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(arccoth(I/sqrt(z)),z = -infinity);

ACTUAL:         3/2*I*Pi

                4.712388981*I

EXPECTED:       I*Pi/2

                1.570796327*I

CHECKUP:        fnormal(evalf(Limit(arccoth(I/sqrt(z)),z = -infinity)));

                0.+1.570796327*I


EXAMPLE 2:      limit(arccoth(I/(-z)^(1/3)),z = infinity);

ACTUAL:         1/2*I*Pi

                1.570796327*I

EXPECTED:       -1/2*I*Pi

                -1.570796327*I

CHECKUP:        fnormal(evalf(limit(func,z = 10^50)));

                0.-1.570796327*I

The same problem with

limit(arccoth(HankelH1(1,z)),z = -infinity);

BUG # 33        limit: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(erf(sqrt(-sqrt(1+I/z))), z=infinity);

ACTUAL:         Error, (in int) too many levels of recursion

EXPECTED:       -erf(I)

                -1.650425759*I

CHECKUP:        evalf(Limit(erf(sqrt(-sqrt(1+I/z))), z=infinity));

                -.9855680608e-13-1.650425759*I


EXAMPLE 2:      limit(erfc(sqrt(-sqrt(1+I/z))), z=infinity);

ACTUAL:         Error, (in int) too many levels of recursion

EXPECTED:       erf(I) + 1

                1.+1.650425759*I

CHECKUP:        evalf(Limit(erfc(sqrt(-sqrt(1+I/z))), z=infinity));

                1.000000000+1.650425759*I


EXAMPLE 3:      limit(erfi(sqrt(-sqrt(1+I/z))), z=infinity);

ACTUAL:         Error, (in int) too many levels of recursion

EXPECTED:       Limit[Erfi[Sqrt[-Sqrt[1+I/z]]], z->Infinity]

The same problem with

limit(erf(sqrt(-sqrt(1+I/z))), z=-infinity);
limit(erf(sqrt(-sqrt(1-I/z))), z=-infinity);
limit(erf(1/sqrt(-sqrt(1-I/z))), z=-infinity);
limit(erfi(1/sqrt(-sqrt(1-I/z))), z=-infinity);
limit(erfi(1/sqrt(-sqrt(1-I/z^2))), z=-infinity);
limit(erfi(1/sqrt(-sqrt(1-I/z^3))), z=-infinity);

COMMENT:        Only Derive 5.06 calculates it correctly.

BUG # 34        limit: INVALID MAGNITUDE OF THE REAL-VALUED LIMIT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(StruveH(0,EllipticPi(1/2,z)),z = 0);

ACTUAL:         StruveH(0,EllipticPi(1/2,0))

                .6148427355

EXPECTED:       StruveH(0, Pi/sqrt(2))

                .77733468418002546656412161004184905579430164572297

CHECKUP:        evalf(Limit(StruveH(0,EllipticPi(1/2,z)),z = 0),50);

                .77733468418002546656412161004184905579430164572296


EXAMPLE 2:      limit(StruveL(0,EllipticPi(1/2,z)),z = 0);

ACTUAL:         StruveL(0,EllipticPi(1/2,0))

                .8089409725

EXPECTED:       StruveL(0, Pi/sqrt(2))

                2.3591001975827913005960695139630449059412292612616

CHECKUP:        evalf(Limit(StruveL(0,EllipticPi(1/2,z)),z = 0),50);

                2.3591001975827913005960695139630449059412292612617


COMMENT:        Mathematica 4.2.1 calculates these limits correctly.

BUG # 35        limit: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(sqrt(z)*EllipticPi(1/2,z), z= infinity);

ACTUAL:         Error, (in depends/internal) too many levels of recursion

EXPECTED:       0

CHECKUP:        evalf(Limit(sqrt(z)*EllipticPi(1/2,z), z= 10^20), 50);

                .15707963267948966192313216916397514420986632395039e-9-
                .48223394384398252608809954182423513009224676425905e-8*I


The same problem with

limit(sqrt(z)*EllipticPi(1/3,z), z= infinity);
limit(sqrt(z-1)*EllipticPi(1/2,z), z= infinity);
limit(sqrt(z^2-1)*EllipticPi(1/2,z), z= infinity);
limit(sqrt(z^2-z-1)*EllipticPi(1/2,z), z= infinity);
limit(sqrt(z^2-z-3)*EllipticPi(1/2,z), z= infinity);
limit(sqrt(z^2-I*z-3)*EllipticPi(1/2,z), z= infinity);

BUG # 36        limit: TOO TIME CONSUMING
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


Maple cannot do quickly a REGULAR limit at a FINITE point.


                limit(cot(1/(arccos(-z))),z = 2);

ACTUAL:         It takes 709 seconds to show the answer.

EXPECTED:       It takes less than 0.1 second to show the answer.


HINT:           plot(Re(cot(1/(arccos(-z)))),z = 1..3)
                plot(Im(cot(1/(arccos(-z)))),z = 1..3)

COMMENT:        Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2
                calculate it correctly in some 0.001-0.03 second.

BUG # 37        limit: TRIVIAL LIMIT CANNOT BE DONE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


The following is trivial and correct.

                limit(cos(1/arcsin(z)),z = -1);

                2*cos(1/Pi)^2-1

However, here Maple fails to yield the answer.


                limit(cos(1/arcsin(z)),z = -2);

ACTUAL:         limit(cos(1/arcsin(z)),z = -2);

EXPECTED:       cos(1/arcsin(-2))

                .9770333572-.1163454356*I

CHECKUP:        evalf(Limit(cos(1/arcsin(z)),z = -2));

                .9770333572-.1163454356*I

The same problem with

limit(cosh(1/arccsch(z)),z = -2);
limit(cosh(1/arcsin(z)),z = -2);
limit(cot(1/arcsin(z)),z = -2);
limit(coth(1/(Pi-arccos(z))),z = -2);
limit(coth(1/arcsin(z)),z = -2);
limit(csc(1/arcsin(z)),z = -2);
limit(csch(1/(Pi-arccos(z))),z = -2);
limit(csch(1/arcsin(z)),z = -2);
limit(sec(1/arcsin(z)),z = -2);
limit(sech(1/(Pi-arccos(z))),z = -2);
limit(sech(1/arcsin(z)),z = -2);
limit(sin(1/arcsin(z)),z = -2);
limit(sinh(1/arcsin(z)),z = -2);
limit(tan(1/arcsin(z)),z = -2);
limit(tanh(1/(Pi-arccos(z))),z = -2);
limit(tanh(1/arcsin(z)),z = -2);

COMMENT:        Derive 5.06 and Mathematica 4.2.1 calculate all these limits correctly.

BUG # 38        limit: LINEARITY PROPERTY IS NOT USED
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


Maple calculates these limits correctly.

                limit(arcsech(sqrt(z)),z = -infinity);

                -1/2*I*Pi

                limit(StruveL(0,1/z),z = -infinity);

                0


However, for the sum of these function, Maple yields an invalid result.


                limit(arcsech(sqrt(z))+StruveL(0,1/z),z = -infinity);

ACTUAL:         1/2*I*Pi

                1.570796327*I

EXPECTED:       -1/2*I*Pi

                -1.570796327*I

CHECKUP:        fnormal(evalf(Limit(arcsech(sqrt(z))+StruveL(0,1/z),z = -10^20)));

                0.-1.570796327*I

BUG # 39        limit: DIVEGENT + CONVERGENT = CONVERGENT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


Maple calculates the following limits correctly.

                limit(BesselI(0,z),z = -infinity);

                infinity

                limit(EllipticPi(1/2,1/z),z = -infinity);

                1/2*2^(1/2)*Pi

However, for the sum, Maple produces a finite output.

                limit(BesselI(0,z)+EllipticPi(1/2,1/z),z = -infinity);

ACTUAL:         1/2*2^(1/2)*Pi

EXPECTED:       infinity

CHECKUP:        evalf(limit(BesselI(0,z)+EllipticPi(1/2,1/z),z = -10^10));

                Float(infinity)

The same problem with

limit(KelvinHer(0,z)-Chi(z),z = infinity);
limit(KelvinHer(0,z)-Chi(z),z = -infinity);
limit(KelvinKer(0,z)+arctan(z),z = -infinity);

BUG # 40        limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(sqrt(1/sqrt(z^2+I*z)-1),z = infinity);

ACTUAL:         I

EXPECTED:       -I

CHECKUP:        fnormal(evalf(Limit(sqrt(1/sqrt(z^2+I*z)-1),z = infinity)));

                0.-1.000000000*I

HINT:           plot(Im(func),z = 10^10..10^11);
::::::::::::::::::::::::::::::::::::::::::::::::: 40%

BUG # 41        limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(arccoth(1-sqrt(1-1/z)),z = infinity);

ACTUAL:         1/2*I*Pi

                1.570796327*I

EXPECTED:       -1/2*I*Pi

CHECKUP:        fnormal(evalf(Limit(arccoth(1-sqrt(1-1/z)),z = infinity)));

                0.-1.570796327*I

The same problem with

limit(arccoth(1-1/sqrt(1-I*z^3)),z = 0, left);

BUG # 42        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(coth(1/arcsinh(z)),z = 2);

ACTUAL:         undefined

EXPECTED:       coth(1/arcsinh(2))

                1.667470009

CHECKUP:        evalf(Limit(coth(1/arcsinh(z)),z = 2));

                1.667470009

COMMENT:        Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2
                calculate this limit correctly.

BUG # 43        limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(arccot(1/(-arcsinh(z^(1/2)-1))^(1/2)),z = infinity);

ACTUAL:         -1/2*Pi

                -1.570796327

EXPECTED:       1.570796327

CHECKUP:        evalf(limit(arccot(1/sqrt((-arcsinh(sqrt(z)-1)))),z = 10^200));

                1.570796327+.6589727518e-1*I

BUG # 44        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(ln(1-1/arcsech(z)^2),z = 10^10);

ACTUAL:         undefined

EXPECTED:       ln(1 - 1/(1/2*I*Pi + arcsinh(-1/10000000000*I))^2)

                .3402399399

CHECKUP:        plot(ln(1-1/arcsech(z)^2),z = 10^10-1000..10^10+1000);

COMMENT:        Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2 calculate
                it correctly.

BUG # 45        limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


This answer is correct.

                evalf(limit(arcsinh(1/(I*z)^(1/3)),z = infinity));
                fnormal(evalf(Limit(arcsinh(1/(I*z)^(1/3)),z = 10^50),30));

                0.
                0.-0.*I

However, below, the sign of the answer is invalid.

                evalf(limit(arccosh(1/(I*z)^(1/3)),z = infinity));

ACTUAL:         1/2*I*Pi

                1.570796327*I

EXPECTED:       -1/2*I*Pi

                -1.570796327*I

                fnormal(evalf(Limit(arccosh(1/(I*z)^(1/3)),z = 10^50),30));

CHECKUP:        0.-1.570796327*I

HINT:           plot(Im(arccosh(1/(I*z)^(1/3))),z = 100000..100010);

The same problem with

limit(arccosh(1/(I*z)^(1/4)),z = infinity);
limit(arccosh(1/(I*z)^(1/6)),z = infinity);

BUG # 46        limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(arccoth(z),z = 0);

ACTUAL:         1/2*I*Pi

EXPECTED:       -1/2*I*Pi

                -1.570796327*I

CHECKUP:        fnormal(evalf(Limit(arccoth(z),z = 0)));

                0.-1.570796327*I

HINT:           plot(Im(arccoth(z)),z = -1..1);

The same problem with

limit(arccot(1/(1-z^3)^(1/2)),z = infinity);
limit(arccoth(1/(1+z)^(1/2)),z = infinity);
limit(arccoth(1-(1-I/z^3)^(1/2)),z = infinity);
limit(arccot((-csch(z^(1/2)-1))^(1/2)),z = infinity);
limit(arctanh((z^2+I*z+1)^(1/4)),z = infinity);
limit(-arctanh(-1+(1-ln(1-z^3))^(1/2)),z = infinity);
limit(ln(1+z^(1/3)-z^(2/3))-arccoth(z^(1/2)),z = 0);

BUG # 47        evalf: INVALID MAGNITUDE OF THE REAL PART
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`

                limit(arccot(sqrt(-csch(z-1))), z = 4);

ACTUAL:         -1/2*Pi-I*Re(arccoth(2^(1/2)/(exp(3)-exp(-3))^(1/2)))

                -1.570796327-.3271365711*I

EXPECTED:       arccot(sqrt(-csch(3))))

                1.570796327-.3271365712*I

CHECKUP:        evalf(Limit(arccot(sqrt(-csch(z-1))), z = 4));

                1.570796327-.3271365711*I

HINT:           plot(Re(arccot(sqrt(-csch(z-1)))), z = 3..5);

COMMENT:        Derive 5.06 and Mathematica 4.2.1 calculate the limit correctly.

COMMENT:        Mathematica 4.2.1 produces the negative value of the real part; this is due to
                Mathematica's branch cut defaults. Please note the ideal agreement of the three
                following numbers.

                N[ArcCot[Sqrt[-Csch[3]]]]
                N[Limit[ArcCot[Sqrt[-Csch[z - 1]]], z -> 4]]
                << NumericalMath`NLimit`
                NLimit[ArcCot[Sqrt[-Csch[z - 1]]], z -> 4]

                -1.5708 - 0.327137 I
                -1.5708 - 0.327137 I
                -1.5708 - 0.327137 I

BUG # 48        Maple language: UNDOCUMENTED FEATURE  or  BUG
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      1.......................................................2;

ACTUAL:         1 .. 2

EXPECTED:       The behavior is described in the Help  or  an "Error, `.`
                unexpected" message is generated.


EXAMPLE 2:      sum(n, n=1.........................................2);

ACTUAL:         3

EXPECTED:       The behavior is described in the Help  or  an "Error, `.`
                unexpected" message is generated.

EXAMPLE 3:      int(z, z=1.........................................2);

ACTUAL:         3/2

EXPECTED:       The behavior is described in the Help  or  an "Error, `.`
                unexpected" message is generated.

BUG # 49        limit: TOO TIME-CONSUMING AND HUMAN UNREADABLE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


1) It takes some 4000 seconds to see the answer
2) The answer is too long, 71 screens, at the 1024x760 resolution.

                limit(cot(1/(1-I*z)^(1/2)), z=-1/1000000);

ACTUAL:         (1-354075436047184534392672953650763356584937159685161625650526649066203899209\
                446192633986001095957111771950538774577147252118263203561387850635045190773465\
                1522014893284877499675393132859815232516435452266000*cot(1/(1000000+I)^(1/2))^\
                818+31076448318817750367832764892781363565235901257346067250059286473155861411\
                835104258463507202002931295522457479169706881326876129001673276366061687212907\
                859233049210665125304376265629268535388568868056954214915954536635717417719875\
                *cot(1/(1000000+I)^(1/2))^776+380605941849653864811161109499867660798166907228\
                217004407285922402013505041378805479840928013766981918167908777459375015918401\
                5793571434561310338018210990177370260786687241197277355967000*cot(1/(1000000+I\
                )^(1/2))^844-36753935140485732686754424398266887016977130808589822702429999773\
                757984371834083974513182362408186590220660625314968964464077293965794116827039\
                328790251300969037945514270123995842968421036740777418386336804032359996721180\
                8358244500*cot(1/(1000000+I)^(1/2))^774-82106999666491760131994830553077735291\
                308346086335846952596215698228023390582870804106891798253671025530455502742902\
                478151756589109497159416984080315730316529980616745470296577025323611958500*co\
                t(1/(1000000+I)^(1/2))^838-109166364096788650964372587325759832990651200982672\
                971418103956906253887256672050741136411172446624808079142849267163447885920896\
                758837665036515964575222680935157687158013327982474423594000*cot(1/(1000000+I)\
                ^(1/2))^842+950220356319270753294980984079236890999858643259206760034793059650\
                247281413740131519663097956052254937063084461430635124739824646132076532859598\
                092478745940018090438278341618930326740753536223504156355391524356184404498112\
                19231102187491268621588692883969052837959995486141968208069973335000*cot(1/(10\
                00000+I)^(1/2))^604-4054045444602469280484437321814205997605157487892565294837\
                910983566311533664381839246807456626181537715282646577120801522292321172516690\
                158194864949009231103227496559351340480404814357490334562925023514451688072289\
                8985788044928481041287903984368173201621360076681402214609624600022652890000*c\
                ot(1/(1000000+I)^(1/2))^606+17009248047264793102639470535212956436995409795268\
                484874471403053124046499600608383352503690467332915950690289855592082212856249\
                322455923693835333348719093104730773168383125126453499326457729569291286174042\
                104300960083991026979146420584143405736627164672718061739957301099517396592136\
                745625*cot(1/(1000000+I)^(1/2))^608+215435965165626662827854130326619938649317\
                005068952869473412768472360186197423197213921137769885958324604274548694030583\
                5347560307531646139384600323130896992220095184384757550535127343010974250*cot(\
                1/(1000000+I)^(1/2))^836-70177971592784983941095505339932710409732710170943799\
                662978300593782574365037671219499985077533959210035107327431325462998436109885\
                904447936728558319870597818199549518544734834902170953856877077294517065540967\
                735787073500570328884496911702282270433087935525660421726976611085908381651815\
                00*cot(1/(1000000+I)^(1/2))^610+2427391512439247360308999651851182455144214737\
                218666849453734946080973100097044304232714527393833530834418099060812383914937\
                484965346712290473605440152422846108567090437492112315144433706579696088890173\
                172281625000362925629463430712731520023322071021078012852977870853574330198988\
                352822627500*cot(1/(1000000+I)^(1/2))^596+303864402818184642681578008185108901\
                167476060307595714884161203507744949496733985514602978585908997061110922927314\
                3172761158572219129781644692915010492760820328841656670861392987647554411575*c\
                ot(1/(1000000+I)^(1/2))^840+49652723862542288611507356288962313262134135365982\
                760466293218401264590573209645738216496413657550741717233904208977875190488785\
                709241191057907741240853994820497412977839043739395425167680052468065347826666\
                236435261924418093115402070111198232800077698030595552564950136994320207999678\
                9539150*cot(1/(1000000+I)^(1/2))^600-13582050502974873233640581153002408621675\
                243178694563751094136731273798872746092431799363899929896375971993521984773356\
                424029798967483669293783508306409821668763182742099539488768012018940112979305\
                59268692000*cot(1/(1000000+I)^(1/2))^814-2190307054262206749104917624479241462\
                633320988941699761311545446637063547322640411003629838314808955831662216104873\
                071149524328278780906156638734861067738037200288309977034781678241097827468165\
                986708064946001220299446420176688138310564824748883337405709665245131139695707\
                67809608480571170000*cot(1/(1000000+I)^(1/2))^602-9598511503532512443405345830\
                273286420302873110520719745135666976663560400039290173574380250706440725981402\
                763634981191088611821315594319284783550596692936528917072601959567777390923952\
                604684426688861434308171085202267780483217850327735110835417381510961368133458\
                2249614268937976403547105090000*cot(1/(1000000+I)^(1/2))^586+47548722719494838\
                351305868672478156506513745963652774497988927064976094412947128615990876126339\
                644920260757667021183291459891365996330583850515739205569414223924802339471161\
                379603859103253431858177603917094870391650562344058383875254574879789467218460\
                846592445009045775089905877578345128355000*cot(1/(1000000+I)^(1/2))^588-231691\
                758957655893865020441254872412234496435541919703355110960771388795117641598308\
                047740675817811102920624363961641653750577675085340002433758198358535870891935\
                041574266372154213710962910711156770453411110718919138241283534121560950984821\
                86153097857362594434399792061199746603154143297386000*cot(1/(1000000+I)^(1/2))\
                ^590+1110474432352669457465166626481386187165669366969192020385128190073918091\
                567125109190690470627197624955662628035187945560588854504934966645176433446595\
                980249630395891114142542030802613280585389910562643838579722171259537226066585\
                6243389195127921105374826031979422477736836858930931650116438750*cot(1/(100000\
                0+I)^(1/2))^592-52350640281043963930716867757675991135634703528096067515251686\
                832040058429508839698777913136556665249924061685151449710145054486310968260806\
                893508556033095523141766199047829037839598557503332228123957502302165654541671\
                26964181243078202588521987914769170375952824986694000662745029797956335000*cot\
                (1/(1000000+I)^(1/2))^594-1352174756047738536965732563594024997657263993095977\
                594463124595472949439582756397782101654348412776609179735291350714403392493584\
                549588732331544589527040533322470990719945790249999519709396475018059305000910\
                370897152823983294206171303014085716166595296312128715459066090673792478765425\
                619892500*cot(1/(1000000+I)^(1/2))^578+715353676103130617456988799694007709885\
                607871899879612255099880533962072941312807881495277573842268828360699575165120\
                071274841269782172096252417589376907495774929549024140935582739010989848122639\
                087762030467924228247171146804881355506033257389391905346713731796336991840275\
                407418743443054259250*cot(1/(1000000+I)^(1/2))^580+180487401413966384686434836\
                763987305663867370047079159806946385380722780736266139783954512647940638422552\
                0079389994275197942368824364111633398784129265292392148998455615125*cot(1/(100\
                0000+I)^(1/2))^136-32718467279501535853152782595305511539109510344855478934822\
                019578345603118092997314241231969888303513579468542936280630841669653327239293\
                222697936341414457168675864940487771805828457685108596925600*cot(1/(1000000+I)\
                ^(1/2))^830-372293119223961903756649244903476872987293129208855493149778723070\
                090806809601374366347685136554354290253550021108167072244638544328319597975112\
                371070580351173388996449031240851034213892369101211995742504988275061030387169\
                930748090867007744188492371556667561324885355336076755320399332554632500*cot(1\
                /(1000000+I)^(1/2))^582+255670626520642779562667285146098531757580093903824262\
                951603709019679063761624034068183144852184738977229998207023759283223554682566\
                25547936564562788805622379102959954011029246660235891222624438704100977174000*\
                cot(1/(1000000+I)^(1/2))^812-4801444962415665669159245088581755290717934571976\
                316684382350161984467362636573152427017908918531406287694151536666324511960809\
                991241780663859477568952614305230258936720633266794467393758288596999894878178\
                0286316587422513931487910900*cot(1/(1000000+I)^(1/2))^770+82778379580683978116\
                916427800405049752814046412158263763650621689502916419352746031827293732962522\
                731641689820385636359470766556115789987679701814178930112021587615101708531899\
                271983333006584206847743037715858551205850970054450139424550725875865543691832\
                33910534587050189385786654723962227270000*cot(1/(1000000+I)^(1/2))^572-4688590\
                616092785600416664233412157012402749495925179602618922130552695439071840668420\
                740260256165985189452107470558904157609966923411900677739274481324907857576004\
                01682951576492945097797789398965989669303824800*cot(1/(1000000+I)^(1/2))^810-4\
                599621023480392671596760943712967775393668590066462244799281554227944796059382\
                567996737293619770875319672323310407768426899019382520420972931628494835711413\
                313773155994139426267809434423308858963054686989072564284855823279661142127646\
                895567120200942209080809948431420132475293023060767161060000*cot(1/(1000000+I)\
                ^(1/2))^574+251437616636813132002594676587932613446565126277636772168149132063\
                094627212122951067575267816986569135454913688209337703408836793238321925467775\
                162738528246189752001779208618093534691456020552208714085470824754759593341426\
                5648097168509874524236450424477518359423802864175678296503095265381974375*cot(\
                1/(1000000+I)^(1/2))^576-14590397202856894311383171157581186686377345403857115\
                493563442693236707932790317968782383252319838046923565422845723785114783072309\
                712630479452256612735963543122075356775472324487221372738232303457295888751338\
                5500*cot(1/(1000000+I)^(1/2))^806+53050447932437455453785337257462210036811662\
                153014188653592345898937577613039148767476677758022279474644206932926672464794\
                509524184840938656723250725927591964397544861180560088576802094829366826047689\
                0994095404848501837833524629360375*cot(1/(1000000+I)^(1/2))^768+83780174106114\
                787197235926742818836405360976144873771318721462776229161056647755006801562094\
                875191111332789907951094685466847601037374138173968400274525492746263625441432\
                52033160503739526434752629345833281614125*cot(1/(1000000+I)^(1/2))^808-1465626\
                503583582992395636597644380880894785131824569569272697828983136907765904433617\
                779371209972107899764492633804600349079308636964839781863867779726173456258186\
                921645754161689435735911527428902637558900333495588791966012436931150741657813\
                1819914867608144381132555676459346617611929868005492000*cot(1/(1000000+I)^(1/2\
                ))^570+19975895067014008772036208278251239663233725963657008494001943577835068\
                666222594171298956157076175832664584613618462423799983909556311948077075762570\
                901051084837455759425829129974426910716833921379600104969711778325842729074483\
                4015406349642854061817399878670398476919885270953376210520966007286500*cot(1/(\
                1000000+I)^(1/2))^560-12238389413745237388771049381274571505351483773700965360\
                221691760058049186339709498569871960025736083371366471814255814734760918701027\
                067484245704791885508933422152087625342248354997437449850103252591509429493364\
                992038180257760398124818574169692713395931440416569865024022601148860012379328\
                3370000*cot(1/(1000000+I)^(1/2))^562-57315734304115545577537463085601517911015\
                976048578419558215936513415820619981638267808851277336803232119177504644095916\
                184282679062077077072328181614049381189575144319261171643624035682425089881303\
                59772228052213756632159254331904048000*cot(1/(1000000+I)^(1/2))^766+7377212892\
                329972751203379432221762321760660667866567702589323699739462361464477395296426\
                540886228917947733680082887546688590908648226909032442504602357046606044746490\
                067194041509632539437052041567985369833155735546861607429855531925850068678193\
                7048872606643877592544524270624551185377520304085000*cot(1/(1000000+I)^(1/2))^\
                564-43752531259867495293574938025428545043469992878688302650898750207717140356\
                964032108318592130600774776508557796195017108257236052854145394386723957061916\
                803505501942503084649986325929748573479164570002352873958435342498904441864979\
                675934958113331188245969467706382945040411415780286496452362090000*cot(1/(1000\
                000+I)^(1/2))^566-181510606348072736196081374721357174941930701885513122132454\
                228533266355132472846606495370690828333990271015951474479552104593072387997293\
                470419064971207308141437443325956916309833011512132928579234504510644376907309\
                516321681910513931761137144175315861329456668556852081223528779295217291540632\
                4300*cot(1/(1000000+I)^(1/2))^550+12057858574866545789085142219170091663713241\
                509497858415155046448863222025341322318065437560194200558514906616755904479833\
                350768785342477822173838106417987259652225013812039684237407604101389509006789\
                906486130735330324236827582925425416350298528572085595891764605168456236097079\
                70245096325382860625*cot(1/(1000000+I)^(1/2))^552+6055976766114076551204684095\
                479919488041156113362147146938145805534896632726837397863921521818714988458261\
                237999710379719586694393001541001372807635055318586959815870833727726550171054\
                7321093435890903767182046821840044698908149160712000*cot(1/(1000000+I)^(1/2))^\
                764-78817168146456642584231537861814646601359140223852930023478400769793688182\
                827891256961119984014003924963315928381144120795251746426695975308858282810493\
                483417294441620238274296637516962512578502414258932677244453760891049482130496\
                4059568956131027259116042753739945755143267068628907638707593860000*cot(1/(100\
                0000+I)^(1/2))^554+50692991645690744227404346747794260519060692722237640228659\
                531404436299480348213033148854375614943803835210682175791281529047942553977413\
                375944984734586303888231343017592489142697673185397211275436379448987143388223\
                229135364308897600914722510637429553684945665554162299333791921310292000225599\
                0000*cot(1/(1000000+I)^(1/2))^556-32080802535260592985903154284399749972700288\
                195602291885792103598390586466762709593495989346564913568798399192739267384627\
                425139530211531925835958563912052162390685253232890852993477391627408351795436\
                209661908738301073290390393511344437104174508527164126173023845032885402991578\
                6257792774540180000*cot(1/(1000000+I)^(1/2))^558+11015187296775979294455155403\
                978240784495963807394182197540604838252145377140912411909445168925497610486470\
                004680561977591900367627421371270952160514814435224286044792549420679835027158\
                196812558385109192234383331503826235388526396776083888582876725552469938609200\
                708498628544080357516688561721881000*cot(1/(1000000+I)^(1/2))^540-704992638138\
                103624089681196721554636483767000*cot(1/(1000000+I)^(1/2))^978-793169218490181\
                592183145027315810464166562467445555800447689227120938393070619614711911197988\
                871764559996615802447925445141852801240612344963488132233570418746122561574126\
                321469865028606883181881793301610509339890498622661305585329648645816271832206\
                7063531515188620200395709725486785008024370470000*cot(1/(1000000+I)^(1/2))^542\
                +56201615631197171329448784356842103040314742380010122944597024080467694216511\
                993918891264897579756240180726514985905333665387228637359037304641915490358469\
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                661891919281560107345154944549429318489485675841846364555435042001818596371378\
                9570022078041174391832108698319396000*cot(1/(1000000+I)^(1/2))^374-24301418214\
                664797616065884920314638623020621607732563585380295575337016295543248771968456\
                078013181669902134766740051234763562545451564119640854315676042243033868707149\
                279074599394569241107334893022717625750727321546892547251915493475625783703266\
                534886566154459931250518536738678047720000*cot(1/(1000000+I)^(1/2))^378+890824\
                459835324744072078084859848410197806494328398749407901284433000176002357855264\
                574021960876462899502412095386709588945200050963235284587496684191997953910074\
                798590145852590166091563063821218950744427098290860075695903476115701845271003\
                7292929221058660553429854473789450554733785000*cot(1/(1000000+I)^(1/2))^376-17\
                186395340327287861368731059412452356943592632844004685961070834846898769429708\
                556930346315133403381816955064429915255006588685875595967628926748612551808317\
                400341350893179651399554125040097839467050849492267957944543221150005304598860\
                4109384222380169637853590998893821617010995175880000*cot(1/(1000000+I)^(1/2))^\
                382+65176464396839703213281772261426002942682900593292566835274015619503031442\
                501918880419940158349726275376603105614120747411770559166866129570307385652405\
                422016026902936361851915784926428333574437222197997206828472957546237235240816\
                142772993089787101085646548771017668988967072318150732000*cot(1/(1000000+I)^(1\
                /2))^380-113588988507349391663488785012544688652057520237873490781373849714652\
                776548156910981684423115829724895743537934976986598188234132849673222269197218\
                858127169906105347121887921731227295161470715165336700873539130570646620750769\
                7533912501757760118876851102017574750802564508687438182160497500*cot(1/(100000\
                0+I)^(1/2))^386+44558282077069984941165316071994156320827441881930048213018603\
                648227613564622528088343686303567351432679883783436094336281156885447127910361\
                697283007354763804630756086431644093753796679194813062825169245107829675070727\
                24572878537502293480)

EXPECTED:       cos(1/((1+1/1000000*I))^(1/2))/sin(1/((1+1/1000000*I))^(1/2))

COMMENT:        Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2 calculate this
                limit in 2-3 seconds and show the very short answers from 60
                to 750 symbols long.

BUG # 50        limit: SIMPLE LIMIT RETURNS UNEVALUATED
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


These trivial limits are calculated correctly.

                limit(1/(z-1),z = 1);
                limit(1/(z-1)^(1/2),z = 1);

                undefined
                undefined

However, the following limits of the same nature are returned unevaluated.


                limit(1/(z-1)^(1/3),z = 1);

ACTUAL:         limit(1/(z-1)^(1/3),z = 1)

EXPECTED:       undefined


COMMENT:        seq(limit(1/(z-1)^(1/k),z = 1), k=1..10);

                undefined,
                undefined,
                limit(1/(z-1)^(1/3),z = 1),
                limit(1/(z-1)^(1/4),z = 1),
                limit(1/(z-1)^(1/5),z = 1)
                limit(1/(z-1)^(1/6),z = 1)
                limit(1/(z-1)^(1/7),z = 1)
                limit(1/(z-1)^(1/8),z = 1)
                limit(1/(z-1)^(1/9),z = 1)
                limit(1/(z-1)^(1/10),z = 1)

COMMENT:        MuPAD 2.5.2 returns unevaluated for all these limits.
::::::::::::::::::::::::::::::::::::::::::::::::: 50%

BUG # 51        limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(StruveL(2,z),z = infinity);

ACTUAL:         -infinity

EXPECTED:       infinity

CHECKUP:        evalf(Limit(StruveL(2,z),z = 10^6),20);

                .12100755984539526566e434292

COMMENT:        seq(limit(StruveL(k,z),z = infinity), k=2..11);

                -infinity, -infinity, -infinity, -infinity, -infinity,\
                -infinity, -infinity, -infinity, -infinity, -infinity

BUG # 52        asympt: INVALID FUNCTION IS RETURNED
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      convert(asympt(BesselI(1/3,-z),z, 1), polynom);

ACTUAL:         1/2*I*2^(1/2)/Pi^(1/2)*exp(-z)*(1/z)^(1/2)

EXPECTED:       (1+sqrt(3)*I)*exp(z)/(2*sqrt(2*Pi*z))

CHECKUP:        evalf(subs(z=10^9, (1+sqrt(3)*I)*exp(z)/(2*sqrt(2*Pi*z))));
                evalf(subs(z=10^9, BesselI(1/3,-z)));

                .5048145892e434294477+.8743645172e434294477*I
                .5048145896e434294477+.8743645174e434294477*I

HINT:           func := BesselI(1/3,-z):
                bb := convert(asympt(func,z, 6), polynom);
                plot(abs(bb), z=10..20);
                plot(abs(func), z=10..20);


EXAMPLE 2:      convert(series(BesselI(1/3,-z), z= infinity, 1), polynom);

ACTUAL:         1/2*I*2^(1/2)/Pi^(1/2)*exp(-z)*(1/z)^(1/2)

EXPECTED:       1/4*exp(z)*(1+I*3^(1/2))*2^(1/2)/z^(1/2)/Pi^(1/2)

CHECKUP:        evalf(subs(z=10^9, (1+sqrt(3)*I)*exp(z)/(2*sqrt(2*Pi*z))));
                evalf(subs(z=10^9, BesselI(1/3,-z)));

                .5048145892e434294477+.8743645172e434294477*I
                .5048145896e434294477+.8743645174e434294477*I

BUG # 53        limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(BesselI(1/3,-z),z = infinity);

ACTUAL:         0

EXPECTED:       infinity+infinity*I*3^(1/2)

CHECKUP:        evalf(Limit(BesselI(1/3,-z),z = 100),20);
                evalf(Limit(BesselI(1/3,-z),z = 1000),20);

                .53657616541791312670e42+.92937718063430792012e42*I
                .12427739685615449007e433+.21525476558726023661e433*I

                divAngle := evalf(Limit(BesselI(1/3,-z),z = 1000),20):
                evalf(Im(divAngle)/Re(divAngle));
                evalf(sqrt(3));

                1.732050807
                1.732050808

BUG # 54        product: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                evalf(Product(1+1/n, n=1..infinity));

ACTUAL:         2.000000000

EXPECTED:       infinity

CHECKUP:        seq(evalf(Product(1+1/n, n=1..10^k)), k=1..5);

                11.00000000, 101.0000000, 1001.000000, 10001.00000, 100001.0000

WORKAROUND:     evalf(product(1+1/n, n=1..infinity));

                Float(infinity)

The same problem with

evalf(Product(1+1/(n-1), n=2..infinity));
evalf(Product(1+1/(n+2), n=1..infinity));

BUG # 55        int: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`

                restart;
                int(sqrt(z)*(1-z^2)^(1/3), z= -1..0);

ACTUAL:         Error, (in type/algext) too many levels of recursion

EXPECTED:       16/13*I*3^(1/2)/GAMMA(2/3)*GAMMA(3/4)*sin(1/12*Pi)*GAMMA(11/12)

                .5270334611*I

CHECKUP:        evalf(Int(sqrt(z)*(1-z^2)^(1/3), z= -1..0));

                0.+.5270334606*I

BUG # 56        int: MEANINGLESS OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


The answer to a definite integral depends on the integration variable.


EXAMPLE 1:      int(sqrt(z)*(1-z^2)^(1/3), z=-1..1);

ACTUAL:         16/13*3^(1/2)*sin(1/12*Pi)*(z^(1/2)+(-z)^(1/2))/z^(1/2)/GAMMA(2/3)*GAMMA(3/4)*\
                GAMMA(11/12)

                .5270334609*(z^(1/2)+(-1.*z)^(1/2))/z^(1/2)

EXPECTED:       (16/13+16/13*I)*3^(1/2)*sin(1/12*Pi)/GAMMA(2/3)*GAMMA(3/4)*GAMMA(11/12)

                .5270334609+.5270334609*I

CHECKUP:        evalf(Int(sqrt(z)*(1-z^2)^(1/3), z=-1..1));

                .5270334606+.5270334606*I


EXAMPLE 2:      int(sqrt(z)*(1+I*z)^(1/3), z= -1..1);

ACTUAL:         2/3*(hypergeom([-1/3, 3/2],[5/2],-I)*z^(1/2)+(-z)^(1/2)*hypergeom([-1/3, 3/2],\
                [5/2],I))/z^(1/2)

                .6666666667*((1.039515376+.1842244656*I)*z^(1/2)+(1.039515376-.1842244656*I)*(\
                -1.*z)^(1/2))/z^(1/2)

EXPECTED:       2/3*hypergeom([-1/3, 3/2],[5/2],-I)+2/3*I*hypergeom([-1/3, 3/2],[5/2],I)

                .8158265611+.8158265611*I

CHECKUP:        evalf(Int(sqrt(z)*(1+I*z)^(1/3), z= -1..1));

                .8158265611+.8158265611*I

The same problem with

int(sqrt(z)*(z^2-1)^(1/3), z= -1..1);
int(sqrt(z)*(1-z^2)^(1/4), z=-1..1);
int(sqrt(z)*(1-z^4)^(1/4), z=-1..1);
int(sqrt(z)*(1-z^6)^(1/4), z=-1..1);
int(sqrt(z)*(1-z^4)^(1/3), z=-1..1);
int(sqrt(z)*(1-z^6)^(1/3), z=-1..1);
int(sqrt(z)*(1-I*z)^(1/3), z= -1..1);
int(sqrt(-z)*(1+I*z)^(1/3), z= -1..1);
int(sqrt(-z)*(1-I*z)^(1/3), z= -1..1);
int(sqrt(z)*(1+I*z^2)^(1/3), z= -1..1);
int(sqrt(z)*(1-I*z^2)^(1/3), z= -1..1);
int(sqrt(z)*(I*z^2-1)^(1/3), z= -1..1);
int(sqrt(z)*(I*z^2+1)^(1/3), z= -1..1);
int(sqrt(z)*(1+sqrt(I)*z)^(1/3), z= -1..1);
int(sqrt(z)*(1-sqrt(I)*z)^(1/3), z= -1..1);
int(sqrt(z)/(1+sqrt(I)*z)^(1/3), z= -1..1);
int(sqrt(z)/(1-sqrt(I)*z)^(1/3), z= -1..1);
int((1+sqrt(I)*z)^(1/3)/sqrt(z), z= -1..1);
int((1-sqrt(I)*z)^(1/3)/sqrt(z), z= -1..1);

BUG # 57        int: INVALID MAGNITUDE OF THE REAL-VALUED INTEGRAL
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                int(sin(z)/sqrt(sin(z)+cos(z)), z = 0..1);

ACTUAL:         1-2^(3/4)*EllipticK(1/2*2^(1/2))+1/2*2^(3/4)*EllipticF(2^(1/2)*(2^(1/2)/(2+2^(\
                1/2)))^(1/2), 1/2*2^(1/2)) + 2^(3/4)*EllipticPi(1/2, 1/2*2^(1/2))-1/2*2^(3/4)*\
                EllipticPi(2^(1/2)*(2^(1/2)/(2+2^(1/2)))^(1/2),1/2,1/2*2^(1/2))-2*2^(1/4)+1/2*\
                2^(3/4)*EllipticF(2^(1/2)*(2^(1/2)*(cos(1)+sin(1))/(cos(1)*2^(1/2)+sin(1)*2^(1\
                /2)+2))^(1/2),1/2*2^(1/2))-1/2*2^(3/4)*EllipticPi(2^(1/2)*(2^(1/2)*(cos(1)+sin\
                (1))/(cos(1)*2^(1/2)+sin(1)*2^(1/2)+2))^(1/2),1/2,1/2*2^(1/2))+(cos(1)+sin(1))\
                ^(1/2)

                .3667522890181217179596219379180129921565149408568

EXPECTED:       1+2^(1/4)*EllipticE(1/2*(2^(1/2)-1)^(1/2)*2^(1/4), 2^(1/2))-((cos(1)-sin(1))*(\
                cos(1)+sin(1))^(1/2)+2^(1/4)*EllipticE(1/2*(2^(1/2)-cos(1)-sin(1))^(1/2)*2^(1/\
                4),2^(1/2))*(1-sin(2))^(1/2))/(cos(1)-sin(1))

                .394189453481633709060360647714985535816755861009144

CHECKUP:        evalf(Int(sin(z)/sqrt(sin(z)+cos(z)), z = 0..1), 51);

                .394189453481633709060360647714985535816755861009144

The same problem with

int(sin(z)*sqrt(sin(z)+cos(z)), z = 0..1);
int(cos(z)/sqrt(sin(z)+cos(z)), z = 0..1);
int(cos(z)*(sin(z)+cos(z))^(1/2), z = 0..1);

BUG # 58        int: MEANINGLESS OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


The output contains a substring  trunc(`limit/mrv/Re`(1)) .


                int(sqrt(tan(z)), z= 0..Pi);

ACTUAL:         1/2*I*2^(1/2)*Pi-1/2*I*exp(1/2*I*trunc(`limit/mrv/Re`(1))*Pi)*2^(1/2)*Pi

EXPECTED:       sqrt(2)*Pi*(1+I)/2

                2.221441469+2.221441469*I

CHECKUP:        evalf(Int(sqrt(tan(z)), z= 0..Pi/2))+
                evalf(Int(sqrt(tan(z)), z= Pi/2+1/10^8..Pi-1/10^8, method = _Sinc));

                2.221441469+2.221241468*I

The same problem with

int(sqrt(tan(z)), z= 0..Pi, 'CauchyPrincipalValue');

BUG # 59        int: MEANINGLESS OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


The output contains a substring  trunc(`limit/mrv/Re`(1)) .


                int(sqrt(sinh(z)), z = -1..1);

ACTUAL:         -(-2*(-I*(exp(1)^2-1+2*I*exp(1))/exp(1))^(1/2)*(-I*(-exp(1)^2+1+2*I*exp(1))/ex\
                p(1))^(1/2)*(I*(exp(1)^2-1)/exp(1))^(1/2)*exp(1)*2^(1/2)*sinh(1)^(1/2)*Ellipti\
                cE(1/2*2^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2),1/2*2^(1/2))*exp(-2)-2*(-I*(exp(1)\
                ^2-1+2*I*exp(1))/exp(1))^(1/2)*(-I*(-exp(1)^2+1+2*I*exp(1))/exp(1))^(1/2)*(I*(\
                exp(1)^2-1)/exp(1))^(1/2)*exp(1)*2^(1/2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2)*(\
                I*exp(-1)-I*exp(1)+2)^(1/2),1/2*2^(1/2))+(-I*(exp(1)^2-1+2*I*exp(1))/exp(1))^(\
                1/2)*(-I*(-exp(1)^2+1+2*I*exp(1))/exp(1))^(1/2)*(I*(exp(1)^2-1)/exp(1))^(1/2)*\
                exp(1)*2^(1/2)*sinh(1)^(1/2)*EllipticF(1/2*2^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2\
                ),1/2*2^(1/2))*exp(-2)+(-I*(exp(1)^2-1+2*I*exp(1))/exp(1))^(1/2)*(-I*(-exp(1)^\
                2+1+2*I*exp(1))/exp(1))^(1/2)*(I*(exp(1)^2-1)/exp(1))^(1/2)*exp(1)*2^(1/2)*sin\
                h(1)^(1/2)*EllipticF(1/2*2^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2),1/2*2^(1/2))+2*(\
                -I*exp(-1)+I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1))\
                ^(1/2)*exp(-1)*exp(-1/2*I*trunc(`limit/mrv/Re`(1))*Pi)*((exp(1)^2-1)/exp(1))^(\
                1/2)*EllipticE(1/2*2^(1/2)*(-I*exp(-1)+I*exp(1)+2)^(1/2),1/2*2^(1/2))*exp(1)^2\
                +2*(-I*exp(-1)+I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp\
                (1))^(1/2)*exp(-1)*exp(-1/2*I*trunc(`limit/mrv/Re`(1))*Pi)*((exp(1)^2-1)/exp(1\
                ))^(1/2)*EllipticE(1/2*2^(1/2)*(-I*exp(-1)+I*exp(1)+2)^(1/2),1/2*2^(1/2))-(-I*\
                exp(-1)+I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1))^(1\
                /2)*exp(-1)*exp(-1/2*I*trunc(`limit/mrv/Re`(1))*Pi)*((exp(1)^2-1)/exp(1))^(1/2\
                )*EllipticF(1/2*2^(1/2)*(-I*exp(-1)+I*exp(1)+2)^(1/2),1/2*2^(1/2))*exp(1)^2-(-\
                I*exp(-1)+I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1))^\
                (1/2)*exp(-1)*exp(-1/2*I*trunc(`limit/mrv/Re`(1))*Pi)*((exp(1)^2-1)/exp(1))^(1\
                /2)*EllipticF(1/2*2^(1/2)*(-I*exp(-1)+I*exp(1)+2)^(1/2),1/2*2^(1/2))+4*((exp(1\
                )^2-1)/exp(1))^(1/2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2))*exp(1)^2*exp(-2)+4*(\
                (exp(1)^2-1)/exp(1))^(1/2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2))*exp(1)^2+4*((e\
                xp(1)^2-1)/exp(1))^(1/2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2))*exp(-2)+4*((exp(\
                1)^2-1)/exp(1))^(1/2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2))-2*((exp(1)^2-1)/exp\
                (1))^(1/2)*sinh(1)^(1/2)*EllipticK(1/2*2^(1/2))*exp(1)^2*exp(-2)-2*((exp(1)^2-\
                1)/exp(1))^(1/2)*sinh(1)^(1/2)*EllipticK(1/2*2^(1/2))*exp(1)^2-2*((exp(1)^2-1)\
                /exp(1))^(1/2)*sinh(1)^(1/2)*EllipticK(1/2*2^(1/2))*exp(-2)-2*((exp(1)^2-1)/ex\
                p(1))^(1/2)*sinh(1)^(1/2)*EllipticK(1/2*2^(1/2))+4*I*((exp(1)^2-1)/exp(1))^(1/\
                2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2))-2*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1\
                )^(1/2)*EllipticK(1/2*2^(1/2))*exp(1)^2+4*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1\
                )^(1/2)*EllipticE(1/2*2^(1/2))*exp(1)^2*exp(-2)-2*I*((exp(1)^2-1)/exp(1))^(1/2\
                )*sinh(1)^(1/2)*EllipticK(1/2*2^(1/2))-2*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1)\
                ^(1/2)*EllipticK(1/2*2^(1/2))*exp(-2)+4*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1)^\
                (1/2)*EllipticE(1/2*2^(1/2))*exp(1)^2+4*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1)^\
                (1/2)*EllipticE(1/2*2^(1/2))*exp(-2)-2*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1)^(\
                1/2)*EllipticK(1/2*2^(1/2))*exp(1)^2*exp(-2))/(exp(1)^2+1)/((exp(1)^2-1)/exp(1\
                ))^(1/2)/sinh(1)^(1/2)/(exp(-2)+1)

                -.1566053511-.8472130901*I+(-1.537820820+.8472130832*I)*exp(-1.570796327*I*tru\
                nc(`limit/mrv/Re`(1)))

EXPECTED:       -(1+I)*(-2*(-I*(exp(2)-1+2*I*exp(1)))^(1/2)*(-I*(-exp(2)+1+2*I*exp(1)))^(1/2)*\
                EllipticE(1/2*2^(1/2)*exp(-1/2)*(I-I*exp(2)+2*exp(1))^(1/2),1/2*2^(1/2))-2*I*(\
                -I*(exp(2)-1+2*I*exp(1)))^(1/2)*(-I*(-exp(2)+1+2*I*exp(1)))^(1/2)*EllipticE(1/\
                2*2^(1/2)*exp(-1/2)*(I-I*exp(2)+2*exp(1))^(1/2),1/2*2^(1/2))+(-I*(exp(2)-1+2*I\
                *exp(1)))^(1/2)*(-I*(-exp(2)+1+2*I*exp(1)))^(1/2)*EllipticF(1/2*2^(1/2)*exp(-1\
                /2)*(I-I*exp(2)+2*exp(1))^(1/2),1/2*2^(1/2))+I*(-I*(exp(2)-1+2*I*exp(1)))^(1/2\
                )*(-I*(-exp(2)+1+2*I*exp(1)))^(1/2)*EllipticF(1/2*2^(1/2)*exp(-1/2)*(I-I*exp(2\
                )+2*exp(1))^(1/2),1/2*2^(1/2))+2*exp(2)*EllipticE(1/2*2^(1/2))+2*EllipticE(1/2\
                *2^(1/2))-exp(2)*EllipticK(1/2*2^(1/2))-EllipticK(1/2*2^(1/2))+2*I*exp(2)*Elli\
                pticE(1/2*2^(1/2))+2*I*EllipticE(1/2*2^(1/2))-I*exp(2)*EllipticK(1/2*2^(1/2))-\
                I*EllipticK(1/2*2^(1/2)))/(exp(2)+1)

                .6906077365+.6906077335*I

CHECKUP:        evalf(Int(sqrt(sinh(z)), z = -1..1));

                .6906077360+.6906077360*I

The same problem with

int(sinh(z)^(1/2),z = -1..1);
int(tan(z)^(1/2),z = 0..Pi);
int((-sinh(z-1))^(1/2),z = 0..Pi);
int(tan(z)^(1/2),z = 1..2)
int((-sinh(z-1))^(1/2),z = 1..2)

BUG # 60        int: Error, (in X) must be 3 or 1 real roots for a real cubic
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                int(sqrt(1+I*z^3), z= -1..1);

ACTUAL:         Error, (in int/ellalg/trxstandard) must be 3 or 1 real roots for a real cubic

EXPECTED:       2/5*(1-I)^(1/2)+2/5*(1+I)^(1/2)+3/5*hypergeom([1/3, 1/2],[4/3],-I)+3/5*\
                hypergeom([1/3, 1/2],[4/3],I)

                2.031186687

CHECKUP:        fnormal(evalf(Int(sqrt(1+I*z^3), z= -1..1)));

                2.031186688+0.*I

The same problem with

int(sqrt(1+I*z^3), z= 0..1);
int(sqrt(1+I*z^3)/(z-1), z= 0..1);
int(sqrt(1-I*z^3)/(z-1), z= 0..1);
int(1/((z-1)*sqrt(1+I*z^3)), z= 0..1);
int(1/((z-1)*sqrt(1-I*z^3)), z= 0..1);
int(sqrt(1+I*z^3)/(z^2-1), z= 0..1);
int(sqrt(1-I*z^3)/(z^2-1), z= 0..1);
int(1/((z^2-1)*sqrt(1+I*z^3)), z= 0..1);
int(1/((z^2-1)*sqrt(1-I*z^3)), z= 0..1);
int(sqrt(1+I*z^3)/(z^2-z), z= 0..1);
int(sqrt(1-I*z^3)/(z^2-z), z= 0..1);
int(1/((z^2-z)*sqrt(1+I*z^3)), z= 0..1);
int(1/((z^2-z)*sqrt(1-I*z^3)), z= 0..1);
int(1/sqrt(1+I*z^3), z= -1..1);
int(1/sqrt(1+I*z^3), z= -infinity..infinity);
int(1/sqrt(1+I*z^3), z= 0..1);
int(1/sqrt(1+I*z^3), z= 0..Pi);
int(1/sqrt(1+I*z^3), z= 0..infinity);
int(1/sqrt(1+I*z^3), z= 1..2);
int(1/sqrt(1-I*z^3), z= -1..1);
int(1/sqrt(1-I*z^3), z= -infinity..infinity);
int(1/sqrt(1-I*z^3), z= 0..1);
int(1/sqrt(1-I*z^3), z= 0..Pi);
int(1/sqrt(1-I*z^3), z= 0..infinity);
int(1/sqrt(1-I*z^3), z= 1..2);
int(sqrt(1+I*z^3), z= -1..1);
int(sqrt(1+I*z^3), z= 0..1);
int(sqrt(1+I*z^3), z= 0..Pi);
int(sqrt(1+I*z^3), z= 1..2);
int(sqrt(1-I*z^3), z= -1..1);
int(sqrt(1-I*z^3), z= 0..1);
int(sqrt(1-I*z^3), z= 0..Pi);
int(sqrt(1-I*z^3), z= 1..2);
int(sqrt(z^2+z+1)*sqrt(1+I*z), z= 0..1);
int(sqrt(z^2+z+1)*sqrt(1-I*z), z= 0..1);
int(sqrt(z^2+z+1)/sqrt(1+I*z), z= 0..1);
int(sqrt(z^2+z+1)/sqrt(1-I*z), z= 0..1);
int(sqrt(z^2-z+1)*sqrt(1+I*z), z= 0..1);
int(sqrt(z^2-z+1)*sqrt(1-I*z), z= 0..1);
int(sqrt(z^2-z+1)/sqrt(1+I*z), z= 0..1);
int(sqrt(z^2-z+1)/sqrt(1-I*z), z= 0..1);
int(z/(z-1)*sqrt(1+I*z^3), z= 0..1);
int(z/(z-1)*sqrt(1-I*z^3), z= 0..1);
int(z/(z-1)/sqrt(1+I*z^3), z= 0..1);
int(z/(z-1)/sqrt(1-I*z^3), z= 0..1);
::::::::::::::::::::::::::::::::::::::::::::::::: 60%

BUG # 61        int: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                int(sin(z)*ln(1-z), z= 0..1);

ACTUAL:         undefined

EXPECTED:       gamma*cos(1)-cos(1)*Ci(1)-sin(1)*Si(1);

                -.6665306159

CHECKUP:        evalf(Int(sin(z)*ln(1-z), z= 0..1));

                -.6665306158

HINT:           plot(sin(z)*ln(1-z), z= 0..1);

The same problem with

int(cos(z)*ln(1-z), z=0..1);
int(sin(2*z)*ln(1-z), z= 0..1);
int(cos(2*z)*ln(1-z), z= 0..1);
int(sin(3*z)*ln(1-z), z= 0..1);
int(cos(3*z)*ln(1-z), z= 0..1);
int(sin(z)^2*ln(1-z), z= 0..1);
int(cos(z)*ln(1-z), z= 0..1);
int(cos(z)^2*ln(1-z), z= 0..1);
int(sin(5*z)^3*ln(1-z), z= 0..1);
int(cos(7*z)^4*ln(1-z), z= 0..1);

BUG # 62        int: INVALID MAGNITUDE OF THE REAL AND IMAGINARY PARTS
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                int(sqrt(z)*(I*z)^(1/3), z=0..1);

ACTUAL:         6/11*I

                .5454545455*I

EXPECTED:       3*sqrt(3)/11+3*I/11

                .4723774930+.2727272727*I

CHECKUP:        evalf(Int(sqrt(z)*(I*z)^(1/3), z=0..1));

                .4723774930+.2727272727*I

The same problem with

int(sqrt(z)*(I*z)^(1/4), z=0..1);
int(z^(1/3)*(I*z)^(1/4), z=0..1);
int(z^(1/3)*(I*z)^(3/4), z=0..1);
int(sqrt(z)*(I*z)^(1/5), z=0..1);
int(sqrt(z)*(I*z)^(2/5), z=0..1);
int(sqrt(z)*(I*z)^(3/5), z=0..1);
int(sqrt(z)*(I*z)^(4/5), z=0..1);
int(sqrt(z)*(I*z)^(1/6), z=0..1);
int(sqrt(z)*(I*z)^(1/7), z=0..1);
int(sqrt(z)*(I*z)^(2/7), z=0..1);
int(sqrt(z)*(I*z)^(3/7), z=0..1);
int(sqrt(z)*(I*z)^(4/7), z=0..1);
int(sqrt(z)*(I*z)^(5/7), z=0..1);

BUG # 63        int: INVALID INDEFINITE INTEGRATION
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      restart;
                func := sqrt(1+sqrt(1-z)):
                zero:= simplify(func - diff(int(func, z),z)):
                [coulditbe(zero = 0),is(zero=0)];

ACTUAL:         [true, false]

EXPECTED:       [true, true]


IMPLICATIONS:   Maple calculates incorrectly definite integrals involving  sqrt(sqrt(z)-1)


EXAMPLE 2:      int(sqrt(1+sqrt(1-z)), z= 0..1);

ACTUAL:         8/15*2^(1/2)

                .7542472330

EXPECTED:       8*sqrt(2)/15 + 8/15

                1.287580566

CHECKUP:        evalf(Int(sqrt(1+sqrt(1-z)), z= 0..1));

                1.287580567

The same problem with

int(1/sqrt(1+sqrt(1-z)), z= 0..1);

BUG # 64        plot: INVALID GRAPH
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                plot(abs(z)-sqrt(I*z)*sqrt(-I*z),z = -1..1);

ACTUAL:         Numerous spurious vertical lines.

EXPECTED:       The straight line y = 0 .

COMMENT:        Derive 5.06 and MuPAD 2.5.2 shows the straight line y = 0.

BUG # 65        evalf: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                evalf(Sum(1/n,n = 1..infinity));

                infinity

However, for the following simple sum Maple yields a senseless answer,
actually this sum cannot be negative.

                evalf(Sum(exp(n), n= 0..infinity));

ACTUAL:         -.5819767069

EXPECTED:       infinity

CHECKUP:        seq(evalf(Sum(exp(n), n= 0..k)), k=1000..1002);
                evalf(sum(exp(n), n= 0..infinity));

                .3116606613e435, .8471815123e435, .2302878110e436
                Float(infinity)

COMMENT:        Derive 5.06 and Mathematica 4.2.1 calculate it correctly.

                APPROX(SUM(EXP(n), n, 0, inf))

                inf

                NSum[Exp[n], {n, 0, Infinity}]

                ComplexInfinity

BUG # 66        plot: DISAPPEARED GRAPH
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


One can see only the axes without any vestige of the graph.

plot(exp(z), z= 0..100);

COMMENT:        Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2 draw it
                correctly.

BUG # 67        sum: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                sum(1/(n*(n^4+1)), n= 1..infinity);

ACTUAL:         -infinity*signum(-1+1/4*Sum(1, _alpha = RootOf(_Z^4+1)))+gamma-Sum(-1/4*Psi(1-\
                _alpha),_alpha = RootOf(_Z^4+1))

                Float(undefined)-0.*I

EXPECTED:       gamma-Sum(-1/4*Psi(1-_alpha),_alpha = RootOf(_Z^4+1))

                .5350348873

CHECKUP:        evalf(Sum(1/(n*(n^4+1)), n= 1..infinity));

                .5350348873

The same problem with

sum(1/(n*(1+n^5)), n=1..infinity);
sum(1/(n*(1+n^8)), n=1..infinity);
sum(1/(n*(1+n^10)), n=1..infinity);
sum(1/(n*(1+n^11)), n=1..infinity);

COMMENT:        Maple also yields invalid outputs for

                evalf(sum(1/(n*(1+n^6)), n=1..infinity));
                evalf(sum(1/(n*(1+n^7)), n=1..infinity));
                evalf(sum(1/(n*(1+n^9)), n=1..infinity));
                evalf(sum(1/(n*(1+n^12)), n=1..infinity));

                Float(-infinity)+0.*I
                Float(-infinity)-0.*I
                Float(infinity)+0.*I
                Float(infinity)-0.*I

COMMENT:        Mathematica 4.2.1 calculates these sums correctly.

BUG # 68        sum: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                sum(1/(n*(n^3-2)), n=2..infinity);

ACTUAL:         signum(1/6*Sum(1,_alpha = RootOf(_Z^3-2))-1/2)*infinity-Sum(1/6*Psi(2-_alpha),\
                _alpha = RootOf(_Z^3-2))+1/2-1/2*gamma

                Float(infinity)-0.*I

EXPECTED:       1/2-1/2*gamma-Sum(1/6*Psi(2-_alpha),_alpha = RootOf(_Z^3-2));

                .1043077220

CHECKUP:        evalf(Sum(1/(n*(n^3-2)), n=2..infinity));

                .1043077220

The same problem with

> evalf(sum(1/(n*(n^3-2)), n=2..infinity));
  evalf(sum(1/(n*(n^4-2)), n=2..infinity));
  evalf(sum(1/(n*(n^5-2)), n=2..infinity));
  evalf(sum(1/(n*(n^3-3)), n=2..infinity));
  evalf(sum(1/(n*(n^4-3)), n=2..infinity));
  evalf(sum(1/(n*(n^5-3)), n=2..infinity));

Float(infinity)-0.*I
Float(undefined)-0.*I
Float(undefined)-0.*I
Float(undefined)-0.*I
Float(undefined)-0.*I
Float(infinity)-0.*I

COMMENT:        Mathematica 4.2.1 calculates these sums correctly.

BUG # 69        evalf: ADDITIVITY PROPERTY FAILS
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


These two approximations are valid.

                evalf(Sum(1/(2^n),n = 0 .. infinity));

                2.000000000

                evalf(Sum((-1)^n/(2^(n+1)),n = 0 .. infinity));

                .3333333333

However, an attempt to approximate the sum of the summands does
not return a number despite the fact that the summand has none
singularity over the summation region.

                evalf(Sum(1/(2^n)+(-1)^n/(2^(n+1)),n = 0 .. infinity));

ACTUAL:         Sum(1/(2^n)+(-1)^n/(2^(n+1)),n = 0 .. infinity)

EXPECTED:       2.333333333     # 2.000000000 + .3333333333

CHECKUP:        evalf(sum(1/(2^n)+(-1)^n/(2^(n+1)),n = 0 .. infinity));

                2.333333333

BUG # 70        sum: Error, (in sum/polynom) wrong number (or type) ...
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`

These sums are okay.

                sum(harmonic(n), n=2..infinity);
                sum(Heaviside(n), n=2..infinity);

                infinity
                infinity

However, the sum of their summands invokes an error message.

                sum(harmonic(n)*Heaviside(n), n=2..infinity);

ACTUAL:         Error, (in sum/polynom) wrong number (or type) of parameters
                in function series

EXPECTED:       infinity

CHECKUP:        evalf(Sum(harmonic(n)*Heaviside(n), n=2..1000));

                6491.956331
::::::::::::::::::::::::::::::::::::::::::::::::: 70%

BUG # 71        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(exp((1-z)^(2/3)),z = infinity);

ACTUAL:         exp(-infinity+infinity*I*3^(1/2))

                evalf(%);

                undefined+undefined*I

EXPECTED:       0

CHECKUP:        limit(exp((1-z)^(2/3)),z = 1000000.);

                -.1464858820e-2171+.3047113864e-2171*I

COMMENT:        Derive 5.06, Mathematica 4.2.1 and MuPAD 2.5.2 calculate
                this limit correctly.

                LIM(EXP((1 - z)^(2/3)), z, inf)

                0

                Limit[Exp[(1 - z)^(2/3)], z -> Infinity]

                0

                limit(exp((1-z)^(2/3)),z = infinity);

                0

BUG # 72        limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(StruveL(0,z),z = infinity);

ACTUAL:         0

EXPECTED:       infinity

CHECKUP:        evalf(limit(StruveL(0,z),z = 10^6), 20);

                .12100780186087797958e434292


EXAMPLE 2:      limit(StruveL(1,z),z = infinity);

ACTUAL:         -2/Pi

EXPECTED:       infinity

CHECKUP:        evalf(limit(StruveL(1,z),z = 10^6), 20);

                .12100774135696192315e434292

EXAMPLE 3:      limit(StruveH(1,I*z),z = infinity);

ACTUAL:         2/Pi

EXPECTED:       -infinity

CHECKUP:        evalf(limit(StruveH(1,I*z),z = 10^10));

                Float(-infinity)

WORKAROUND:     limit(convert(series(StruveL(0,z),z = infinity,1), polynom),\
                z=infinity);

                infinity

                limit(convert(asympt(StruveL(0,z),z), polynom), z=infinity);

                infinity

The same problem with

limit(StruveL(1,z),z = -infinity);
limit(StruveH(0,I*z),z = infinity);
limit(StruveL(1,z)/arcsec(z),z = -infinity);
limit(StruveL(1,z)*arcsec(z),z = -infinity);

BUG # 73        plot: GRAPH IS TOTALLY ABSENT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                plot(Im(StruveH(0,I*z)),z = 0..100);

ACTUAL:         Only the axes are shown; none vestige of the graph can be seen.

EXPECTED:       Both the axes and graph are shown.

The same problem with

plot(Im(StruveH(2,I*z)),z = 0..100);
plot(Im(StruveH(4,I*z)),z = 0..100);
plot(Im(StruveH(6,I*z)),z = 0..100);

COMMENT:        Mathematica 4.2.1 draws both the axes and graphs correctly.

                Plot[Im[StruveH[0, I*z]], {z, -100, 0}]
                Plot[Im[StruveH[2, I*z]], {z, -100, 0}]
                Plot[Im[StruveH[4, I*z]], {z, -100, 0}]
                Plot[Im[StruveH[6, I*z]], {z, -100, 0}]

BUG # 74        plot: GRAPH IS TOTALLY ABSENT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                plot(BesselI(0,z), z = -100..0);

ACTUAL:         Only the axes are shown; none vestige of the graph can be seen.

EXPECTED:       Both the axes and graph are shown.

The same problem with

plot(BesselI(1,z), z = -100..0);
plot(BesselI(2,z), z = -100..0);
plot(BesselI(3,z), z = -100..0);
plot(BesselI(4,z), z = -100..0);
plot(BesselI(5,z),z = -100..0);

COMMENT:        Mathematica 4.2.1 and MuPAD draw both the axes and graphs correctly.

                Table[Plot[BesselI[k, z], {z, -100, 0}], {k, 0, 5}]
                plotfunc2d(besselI(0,z),besselI(1,z),besselI(2,z),besselI(3,z),besselI(4,z),\
                besselI(5,z),z = -100..0);

BUG # 75        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`

                limit(tanh(arcsec(z)),z = 1/2);

ACTUAL:         undefined

EXPECTED:       tanh(arcsec(1/2))

                3.854535294*I

HINT:           plot(Re(tanh(arcsec(z))),z = 1/2..1);
                plot(Im(tanh(arcsec(z))),z = 1/2..1);

WORKAROUND:     limit(simplify(convert(series(tanh(arcsec(z)),z = 1/2,1), polynom)), z=1/2);

                (exp(Pi)*(2*I+I*3^(1/2))^(2*I)-1)/(exp(Pi)*(2*I+I*3^(1/2))^(2*I)+1)

                .2614497841e-8+3.854535294*I

BUG # 76        limit: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(BesselY(2,sqrt(z))-sqrt(sec(z-1)), z=-infinity);

ACTUAL:         Error, (in type/radalgnum) too many levels of recursion

EXPECTED:       undefinite

BUG # 77        evalf: Error, (in X) invalid assignment to Digits
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                evalf(limit(BesselY(0, sqrt(z)),z = -10^20));

ACTUAL:         Error, (in evalf/Bessel/asymptJY) invalid assignment to Digits

EXPECTED:       undefined

CHECKUP:        seq(evalf(limit(BesselY(0,sqrt(z)),z = -10^k)), k=17..19);

                0.+.1410271793e137335970*I,
                0.+.1009629179e434294478*I,
                .1003286720e1373359701+.6836559561e1373359733*I

HINT:           plot(Im(BesselY(0,sqrt(z))), z=-1000..-800);
                plot(Re(BesselY(0,sqrt(z))), z=-1000..-800);

BUG # 78        limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(BesselY(0, sqrt(z)),z = -infinity);

ACTUAL:         0

EXPECTED:       I*infinity

CHECKUP:        evalf(limit(BesselY(0,sqrt(z)),z = -10000), 30);

                0.+.107375170713107382351972085760e43*I

HINT:           plot(Im(BesselY(0,sqrt(z))), z=-1000..-800);
                plot(Re(BesselY(0,sqrt(z))), z=-1000..-800);


EXAMPLE 2:      limit(BesselY(1, sqrt(z)),z = -infinity);

ACTUAL:         0

EXPECTED:       -infinity

CHECKUP:        evalf(limit(BesselY(1,sqrt(z)),z = -10000), 30);

                -.106836939033816248120614576322e43+0.*I

The same problem with

limit(BesselY(2, sqrt(z)),z = -infinity);
limit(BesselY(3, sqrt(z)),z = -infinity);
limit(BesselY(4, sqrt(z)),z = -infinity);
limit(BesselY(5, sqrt(z)),z = -infinity);
limit(BesselY(6, sqrt(z)),z = -infinity);
limit(BesselY(1/3,z^(1/2))*Shi(1/z),z = -infinity);

BUG # 79        limit: INVALID MAGNITUDE OF THE IMAGINARY PART
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(tan(-1+sqrt(1-BesselI(1/3,z))), z=-infinity);

ACTUAL:         0

EXPECTED:       -I

CHECKUP:        evalf(limit(tan(-1+sqrt(1-BesselI(1/3,z))), z=-1000));

                0.-1.000000000*I

COMMENT:        Mathematica 4.2.1 calculates it correctly.

The same problem with

limit(tan(-1+sqrt(1-BesselI(2/3,z))), z=-infinity);
limit(tan(-1+sqrt(1-BesselI(1/4,z))), z=-infinity);
limit(tan(-1+sqrt(1-BesselI(1/5,z))), z=-infinity);
limit(tan(-1+sqrt(1-BesselI(2/5,z))), z=-infinity);
limit(tan(-1+sqrt(1-BesselI(3/5,z))), z=-infinity);

BUG # 80        limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(sqrt(sin(BesselK(0,z))+cos(BesselK(0,z))),z = -infinity);

ACTUAL:         1

EXPECTED:       undefined

CHECKUP:        seq(evalf(limit(sqrt(sin(BesselK(0,z))+cos(BesselK(0,z))),\
                z = -k)), k=10..15);

                .5482176791e1921-.2270734880e1921*I,
                .1027104357e4973-.4254367986e4972*I,
                .4199489742e12927-.1739480193e12927*I,
                .2170490296e33731-.8990455280e33730*I,
                .5054780882e88288-.2093757979e88288*I,
                .4754790048e231705-.1969498250e231705*I

The same problem with

limit(sqrt(sin(BesselK(1,z))+cos(BesselK(0,z))),z = -infinity);
limit(sqrt(sin(BesselK(1,z))+cos(BesselK(1,z))),z = -infinity);
limit(sqrt(sin(BesselK(1/3,z))+cos(BesselK(1/3,z))),z = -infinity);
limit(sqrt(sin(BesselK(2/3,z))+cos(BesselK(1/4,z))),z = -infinity);
limit(1/sqrt(2*sin(BesselK(1/4,z))+cos(2*BesselK(1/4,z))),z = -infinity);
::::::::::::::::::::::::::::::::::::::::::::::::: 80%

BUG # 81        limit: INVALID MAGNITUDE OF THE REAL-VALUED LIMIT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(StruveL(0, z)/(1-StruveL(0, z)),z = infinity);

ACTUAL:         0

EXPECTED:       -1

CHECKUP:        evalf(Limit(StruveL(0, z)/(1-StruveL(0, z)),z = infinity));

                -1.000000000


EXAMPLE 2:      limit(StruveL(1, z)/(1-StruveL(1, z)),z = infinity);

ACTUAL:         -2/(Pi+2)

                -0.3889845296

EXPECTED:       -1

CHECKUP:        evalf(Limit(StruveL(1, z)/(1-StruveL(1, z)),z = infinity));

                -1.000000000

BUG # 82        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(tan(-1+sqrt(1-BesselI(1/2,z))), z=-infinity);

ACTUAL:         undefined

EXPECTED:       -I

CHECKUP:        evalf(limit(tan(-1+sqrt(1-BesselI(1/2,z))), z=-100));

                0.-1.000000000*I

HINT:           plot(Im(tan(-1+sqrt(1-BesselI(1/2,z)))), z=-900..-1000);
                plot(Re(tan(-1+sqrt(1-BesselI(1/2,z)))), z=-900..-1000);

BUG # 83        limit: TRIVIAL LIMIT CANNOT BE DONE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(sec(z)*cos(z),z = infinity);

ACTUAL:         limit(sec(z)*cos(z),z = infinity);

EXPECTED:       1

WORKAROUND:     limit(simplify(sec(z)*cos(z)),z = infinity);

                1

HINT:           plot(sec(z)*cos(z),z = 0..10^10);
                plot(sec(z)*cos(z),z = -infinity..infinity);


EXAMPLE 2:      limit(csc(z)*sin(z),z = infinity);

ACTUAL:         limit(csc(z)*sin(z),z = infinity)

EXPECTED:       1

WORKAROUND:     limit(simplify(csc(z)*sin(z)),z = infinity);

                1

HINT:           plot(csc(z)*sin(z), z= 0..10^10);
                plot(csc(z)*sin(z), z= -infinity..infinity);

COMMENT:        Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2 calculate the limits correctly.

BUG # 84        limit: TRIVIAL LIMIT CANNOT BE DONE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


The argument of the limits shown below is a smooth function at the limit point so it is enough
just so substitute the proper value of the variable into the function to get the valid answer.


Maple calculates this trivial limit correctly.

                limit(arccsc(1/z)^2,z = 1);

                1/4*Pi^2     ## = arccsc(1/z)^2


However, this trivial limit is returned unevaluated.


                limit(arccsc(1/z)^2,z = 2);

ACTUAL:         limit(arccsc(1/z)^2,z = 2)

EXPECTED:       arccsc(1/2)^2   or   -ln(-2*I+I*3^(1/2))^2

                .7330229932-4.137345261*I

CHECKUP:        evalf(Limit(arccsc(1/z)^2,z = 2));

                .7330229980-4.137345254*I

WORKAROUND:     subs(z=2, arccsc(1/z)^2);

COMMENT:        Derive 5.06 and Mathematica 4.2.1 6 calculate it correctly.

                LIM(ACSC(1/z)^2, z, 2)

                - LN(2 - SQRT(3))^2 + pi^2/4 + pi*#I*LN(2 - SQRT(3))

                0.7330229980 - 4.137345254*#I

                Limit[ArcCsc[1/z]^2, z -> 2]

                ArcSin[2]^2

                0.733023 - 4.13735 I

BUG # 85        limit: TRIVIAL LIMIT CANNOT BE DONE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


Many integrals in Maple are computed via StruveL/StruveH functions.

The argument of the limits shown below is a smooth function at the limit
point so it is enough just so substitute z = 1 into the function.

                limit(StruveL(2,z), z = 1);

ACTUAL:         limit(StruveL(2,z), z = 1);

EXPECTED:       StruveL(2,1)

COMMENT:        If n is add all is right.

                seq(limit(StruveL(2*k+1,z), z = 1), k=0..5);

                StruveL(1,1), StruveL(3,1), StruveL(5,1), StruveL(7,1),
                StruveL(9,1), StruveL(11,1)

                However, at the even n Maple cannot calculate the limit.

                seq(limit(StruveL(2*k,z), z = 1), k=0..5);

                limit(StruveL(0,z),z = 1), limit(StruveL(2,z),z = 1),
                limit(StruveL(4,z),z = 1), limit(StruveL(6,z),z = 1),
                limit(StruveL(8,z),z = 1), limit(StruveL(10,z),z = 1)


COMMENT:        The same holds for StruveH.

BUG # 86        limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(sqrt(-signum(sqrt(z^2+I*z+1)-1)),z = infinity);

ACTUAL:         I

EXPECTED:       -I

CHECKUP:        fnormal(evalf(limit(sqrt(-signum(sqrt(z^2+I*z+1)-1)),z = 10^10)));
                fnormal(evalf(Limit(sqrt(-signum(sqrt(z^2+I*z+1)-1)),z = infinity)));

                0.-1.000000000*I
                0.-1.000000000*I

BUG # 87        limit: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(EllipticPi(2,z)+exp(z), z=-infinity);

ACTUAL:         Error, (in depends/internal) too many levels of recursion

EXPECTED:       0

CHECKUP:        evalf(limit(EllipticPi(2,z)+exp(z), z=-10000));

                .1570796346e-3-.9343828485e-3*I

BUG # 88        evalf: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(EllipticPi(2,z), z=-infinity);

ACTUAL:         infinity

EXPECTED:       0.

CHECKUP:        evalf(Limit(EllipticPi(2,z), z=-10^13));

                .1570796327e-12-.3007345009e-11*I

The same problem with

evalf(Limit(EllipticPi(2,z)*exp(z), z=-infinity));
evalf(Limit(EllipticPi(2,z)+exp(z), z=-infinity));

BUG # 89        limit: Error, (in X) invalid terms in sum
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(Pi-arccot(sin(z)), z=infinity);

ACTUAL:         Error, (in limit/range) invalid terms in sum

EXPECTED:       1/4*Pi .. 3/4*Pi

                .7853981635 .. 2.356194490

HINT:           plot(Pi-arccot(sin(z)), z=0..100);

WORKAROUND:     limit(arctan(sin(z))+Pi/2, z=infinity);

                1/4*Pi .. 3/4*Pi

The same problem with

limit(Pi-arccot(cos(z)), z=infinity);
limit(Pi-arccot(sin(z)), z=-infinity);
limit(Pi-arccot(cos(z)), z=-infinity);
limit(Pi-arccot(cos((z))), z=infinity);
limit(Pi-arccot(cos(sqrt(z))), z=infinity);
limit(Pi-arccot(cos(sqrt(-z))), z=-infinity);
limit(Pi-arccot(cos(sqrt(1-z))), z=-infinity);
limit(Pi-arccot(cos(1+sqrt(1-z))), z=-infinity);
limit(Pi-arccot(cos(-1+sqrt(1-z))), z=-infinity);
limit(Pi-arccot(cos(-1+sqrt(1-z))-1), z=-infinity);
limit(Pi-arccot(cos(-1+(1-z)^(1/2))-1), z=-infinity);

BUG # 90        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit((exp(sqrt(-z))),z = infinity);

ACTUAL:         undefined+undefined*I


EXPECTED:       -1-I .. 1+I

CHECKUP:        seq(evalf(limit(expand((exp(I*sqrt(z)))),z = 10^k)), k=5..10);

                -.4774096142+.8786808654*I, .5623790763+.8268795405*I,\
                -.2615753829+.9651830649*I, -.9521553683-.3056143889*I,\
                .8799440665-.4750776122*I, -.9993608074+.3574879797e-1*I

WORKAROUND:     limit(expand((exp(I*sqrt(z)))),z = infinity);

                -1-I .. 1+I

COMMENT:        Mathematica 4.2.1 calculates it correctly.

                Limit[Exp[Sqrt[-z]], z -> Infinity]

                (1 + I) Interval[{-1, 1}]
::::::::::::::::::::::::::::::::::::::::::::::::: 90%

BUG # 91        limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(tan(sqrt(z)),z = -infinity);

ACTUAL:         undefined

EXPECTED:       I

CHECKUP:        seq(evalf(limit(tan(sqrt(z)),z = -10^k)), k=7..10);

                1.000000000*I, 1.*I, 1.000000000*I, 1.*I

BUG # 92        limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(AiryAi(sqrt(z)),z = -infinity);

ACTUAL:         0

EXPECTED:       undefined

CHECKUP:        seq(evalf(limit(AiryAi(sqrt(z)),z = -10^k)), k=10..13);

                .8684731304e6474078+.8806659285e6474078*I,
                .3812263500e36406425-.3489738753e36406425*I,
                -.5767685690e204728379+.1184876142e204728381*I,
                .1522631815e1151272295-.1019600743e1151272295*I

EXAMPLE 2:      limit(AiryBi(sqrt(z)),z = -infinity);

ACTUAL:         0

EXPECTED:       undefined

CHECKUP:        seq(evalf(limit(AiryBi(sqrt(z)),z = -10^k)), k=10..13);

                -.8806659285e6474078+.8684731304e6474078*I,
                .3489738753e36406425+.3812263500e36406425*I,
                -.1184876142e204728381-.5767685658e204728379*I,
                .1019600742e1151272295+.1522631815e1151272295*I

BUG # 93        limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(FresnelS((-z)^(1/3)),z = infinity);

ACTUAL:         1/2

EXPECTED:       undefined

CHECKUP:        evalf(Limit(FresnelS((-z)^(1/3)),z = 1000));

                .9550051175e57-.1660299772e58*I

The same problem with

limit(FresnelC((-z)^(1/3)),z = infinity);
limit(FresnelS((-z)^(2/3)),z = infinity);
limit(FresnelC((-z)^(2/3)),z = infinity);
limit(FresnelS((-z)^(1/4)),z = infinity);
limit(FresnelC((-z)^(1/4)),z = infinity);
limit(FresnelS((-z)^(3/4)),z = infinity);
limit(FresnelC((-z)^(3/4)),z = infinity);

BUG # 94        int: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                int(exp(-2*z + abs(1-z^2)), z= 0..infinity);

ACTUAL:         undefined

EXPECTED:       infinity

CHECKUP:        evalf(Int(exp(-2*z + abs(1-z^2)), z= 0..infinity));

                Float(infinity)

BUG # 95        limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(cos(sqrt(1-z))/(1-z), z = infinity);

ACTUAL:         0

EXPECTED:       -infinity

CHECKUP:        evalf(Limit(cos(sqrt(1-z))/(1-z),z = 10000));

                -.1337488633e40

The same problem with

limit(cos(-1+sqrt(1-z))/(1-z),z = infinity);
limit(cos(1+sqrt(1-z))/(1-z),z = infinity);
limit(cos(-1+sqrt(1-z))/(1-z),z = infinity);
limit(cos(-1+sqrt(1-z))/(1-z^(1/3)),z = infinity);
limit(cos(-1+sqrt(1-z))*ln(z)/(1-z^(1/3)),z = infinity);

BUG # 96        limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      limit(FresnelS(z),z = -infinity);

ACTUAL:         1/2

EXPECTED:       -1/2

CHECKUP:        seq(evalf(limit(FresnelS(z),z = -10^k)), k=100..103);

                -.5000000000, -.5000000000, -.5000000000, -.5000000000


EXAMPLE 2:      limit(FresnelC(z),z = -infinity);

ACTUAL:         1/2

EXPECTED:       -1/2

CHECKUP:        seq(evalf(limit(FresnelC(z),z = -10^k)), k=100..103);

                -.5000000000, -.5000000000, -.5000000000, -.5000000000

The same problem with

limit(FresnelS(z)*Si(z),z = -infinity);
limit(FresnelS(z)*Ci(z),z = -infinity);
limit(FresnelC(z)*Si(z),z = -infinity);
limit(FresnelC(z)*Ci(z),z = -infinity);
limit(FresnelS(z)*arctan(z),z = -infinity);
limit(FresnelC(z)*arctan(z),z = -infinity);
limit(FresnelS(z+arctan(z)),z = -infinity);
limit(FresnelC(z+arctan(z)),z = -infinity);
limit(BesselJ(1,FresnelC(z)),z = -infinity);
limit(BesselJ(1,FresnelS(z)),z = -infinity);

A similar problem with

limit(FresnelS(sqrt(-z)),z = infinity);
limit(FresnelC(sqrt(-z)),z = infinity);

BUG # 97        limit: INVALID DIVERGENCE TYPE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                limit(1/KelvinKer(0,z),z = infinity);

ACTUAL:         -infinity

EXPECTED:       -infinity..infinity   or   undefined

CHECKUP:        seq(evalf(limit(1/KelvinKer(0,z),z = 10^k)), k=4..9);

                -.6967140106e3073-0.*I,
                .4587483394e30712-0.*I,
                -.3724641372e307096-0.*I,
                -.1408425312e3070930-0.*I,
                .1635087033e30709262-0.*I,
                -.3393380936e307092578-0.*I

BUG # 98        int: INVALID MAGNITUDE OF THE REAL-VALUED INTEGRAL
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


EXAMPLE 1:      int(sin(z)*arctanh(z), z= 0..1);

ACTUAL:         1/2*Pi^(3/2)*(4/Pi^(3/2) - 4/Pi^(3/2)*Sum((-1)^(2*_k2)*(-Pi*tan(Pi*_k2)-Psi(1+\
                _k2)-Psi(5/2+_k2)-2*ln(2))*2^(-2*_k2)*cos(Pi*_k2)*2^(2*_k2)*(1+_k2)/GAMMA(4+2*\
                _k2),_k2 = 0 .. infinity))

                2.411313648

EXPECTED:       -1/2*cos(1)*(gamma-Ci(2)+ln(2))+1/2*sin(1)*Si(2)

                .4465329907

CHECKUP:        evalf(Int(sin(z)*arctanh(z), z= 0..1));

                .4465329905


EXAMPLE 2:      int(cos(z)*arctanh(z), z= 0..1);

ACTUAL:         1/2*Pi^(3/2)*(2/Pi^(1/2)*cos(1)-2/Pi^(1/2)*sin(1))

                -.9461493090

EXPECTED:       1/2*(gamma-2*Ci(1)+Ci(2)+ln(2))*sin(1)+1/2*cos(1)*(2*Si(1)-Si(2))

                .5060008712

CHECKUP:        evalf(Int(cos(z)*arctanh(z), z= 0..1));

                .5060008712

COMMENT:        Mathematica 4.2.1 calculates these integrals correctly.

BUG # 99        int: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


                int(sin(z)/2^z, z=0..infinity);

ACTUAL:         undefined

EXPECTED:       1/(1+ln(2)^2))

                .6754689210

The same problem with

int(cos(z)/2^z, z=0..infinity);

BUG # 100       simplify: IDENTITY IS BROKEN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`


This bug was introduced in `Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223` .


The following 4 expressions are simplified correctly into 0.

                expr := sqrt((99+I)^(3/2)): evalf(expr - simplify(expr));

                expr := sqrt((99-I)^(3/2)): evalf(expr - simplify(expr));

                expr := sqrt((99*I)^(3/2)): evalf(expr - simplify(expr));

                expr := sqrt((99/I)^(3/2)): evalf(expr - simplify(expr));

                0.-.1e-9*I
                0.+.1e-9*I
                0.-.1e-7*I
                0.+.1e-7*I


However, their counterparts show TERRIBLE bug manifestations!


                expr := sqrt((100+I)^(3/2)): evalf(expr - simplify(expr));

                expr := sqrt((100-I)^(3/2)): evalf(expr - simplify(expr));

                expr := sqrt((100*I)^(3/2)): evalf(expr - simplify(expr));

                expr := sqrt((100/I)^(3/2)): evalf(expr - simplify(expr));

ACTUAL:         -28.46076575-.2134526304*I      #   <---------------------------------
                -28.46076575+.2134526304*I      #   <--  All these 4 numbers must be  
                -10.89136142-26.29407246*I      #   <--  equal to zero identically    
                -10.89136142+26.29407246*I      #   <---------------------------------

EXPECTED:       0.
                0.
                0.
                0.

COMMENT:        Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2 calculate it
                correctly.

The same problem with

                expr := 1/10709*sqrt(10709)*sqrt(32230+10*I-1103027/(103-10*I)^(3/2)+107090*I/\
                (103-10*I)^(3/2)):

                evalf(expr);
                evalf(simplify(expr));

ACTUAL:         .9088156160e-1-2.611004196*I
                1.706291978-.1119792733e-2*I

EXPECTED:       1.706291978-.1119792733e-2*I
                1.706291978-.1119792733e-2*I


IMPLICATION:    evalf(limit((1/(z^2-I*z+3)-1/(z^2-I*z+3)^(1/2)+3)^(1/2),z = 10));


ACTUAL:         .9088156160e-1-2.611004196*I

EXPECTED:       1.706291978-.1119792733e-2*I


COMMENT:        seq(evalf(limit((1/(z^2-I*z+3)-1/(z^2-I*z+3)^(1/2)+3)^(1/2),
                z = k)), k =1..10);

                1.657258306-.4070486549e-3*I,
                1.662844802-.4110381255e-2*I,
                1.672198935-.4524844638e-2*I,
                1.680681699-.3835496552e-2*I,
                1.687556357-.3070973420e-2*I,
                1.693021914-.2446838594e-2*I,
                1.697394301-.1969780540e-2*I,
                1.700939497-.1608623980e-2*I,
                1.703856885-.1333012836e-2*I,
                .9088156160e-1-2.611004196*I

expr :=1/1709*sqrt(10709)*sqrt(32230+10*I-1103027/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.5694854553-16.36117258*I
10.69203089-.7016887291e-2*I

expr := 1/1709*sqrt(10709)*sqrt(3223+10*I-1103027/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.4818240181-19.33786916*I
2.821844747-.2658713805e-1*I

expr := 1/1709*sqrt(10709)*sqrt(3223+10*I-110327/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

2.543303771+6.170050035*I
3.374313545+.5188398623e-1*I

expr := 1/1709*sqrt(1709)*sqrt(3223+10*I-110327/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

1.016002572+2.464820277*I
1.347975527+.2072668789e-1*I

expr := 1/1709*sqrt(189)*sqrt(3223+10*I-110327/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.3378739259+.8196814914*I
.4482722740+.6892706377e-2*I

expr := 1/1709*sqrt(189)*sqrt(3223+10*I-11327/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.5864760130+.5472823080*I
.4549530485+.7759039308e-2*I

expr := 1/179*sqrt(189)*sqrt(3223+10*I-11327/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

5.599371544+5.225170193*I
4.343657877+.7407931944e-1*I

expr := 1/179*sqrt(189)*sqrt(3223+10*I-11327/(103-10*I)^(3/2)+17090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

3.577207487+1.204307534*I
4.351448828+.1661035412e-1*I

expr := 1/179*sqrt(189)*sqrt(3223+10*I-11327/(103-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

3.567417936-.1051135961*I
4.352994237+.5846248394e-2*I

expr := 1/179*sqrt(189)*sqrt(3223+10*I-1327/(103-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

4.273152266+.7095780736e-2*I
4.359359359+.6767448511e-2*I

expr := 1/179*sqrt(189)*sqrt(323+10*I-1327/(103-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

1.074415515+.2822125249e-1*I
1.377758712+.2141284980e-1*I

expr := 1/179*sqrt(89)*sqrt(323+10*I-1327/(103-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.7372866537+.1936602042e-1*I
.9454471721+.1469395048e-1*I

expr := 1/179*sqrt(89)*sqrt(323+10*I-1327/(13-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.9269541531+.1780782420e-1*I
.9308404777-.9617677861e-2*I

expr := 1/179*sqrt(89)*sqrt(33+10*I-1327/(13-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.2410132201+.6849017073e-1*I
.2492610255-.3591625958e-1*I

expr := sqrt(89)*sqrt(33+10*I-1327/(13-10*I)^(3/2)+197*I/(101-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

43.16247440+12.80979177*I
44.61565061-6.423929822*I

expr := sqrt(89)*sqrt(33+10*I-137/(13-10*I)^(3/2)+197*I/(101-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

55.36458611+21.97402995*I
53.68513721+7.023786746*I

expr := sqrt(89)*sqrt(33+10*I-137/(13-10*I)^(3/2)+97*I/(101-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

54.05776912+14.54242933*I
53.68663849+6.943411760*I

expr := sqrt(89)*sqrt(33+10*I-17/(13-10*I)^(3/2)+97*I/(101-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

55.12969449+15.47364059*I
54.66113471+8.044001111*I

expr := sqrt(89)*sqrt(13+10*I-17/(13-10*I)^(3/2)+97*I/(101-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));

38.77848308+21.99820650*I
35.95400873+12.22935200*I

expr := sqrt(89)*sqrt(13+10*I-17/(13-10*I)^(3/2)+97*I/(101-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

39.94907946+21.54482542*I
35.96860209+12.22651401*I

expr := sqrt(89)*sqrt(13+I-17/(13-10*I)^(3/2)+97*I/(101-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

35.98964102+12.78690005*I
33.84669659+1.160249635*I

expr := sqrt(29)*sqrt(13+I-17/(13-10*I)^(3/2)+97*I/(101-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

20.54383462+7.299099203*I
19.32058553+.6623010384*I

expr := sqrt(29)*sqrt(2+I-17/(13-10*I)^(3/2)+97*I/(101-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

13.29995017+11.27459013*I
7.532100287+1.698867956*I

expr := sqrt(29)*sqrt(2+I-17/(3-10*I)^(3/2)+97*I/(101-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

13.36197413+10.93942120*I
8.013219032+1.125243166*I

expr := sqrt(29)*sqrt(2+I-17/(3-10*I)^(3/2)+97*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

13.43587731+11.03426592*I
8.013513923+1.127800842*I

expr := sqrt(29)*sqrt(2+I-17/(3-10*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

12.90718557+10.36304628*I
8.011301768+1.110016225*I

expr := sqrt(29)*sqrt(2+I-17/(3-7*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

12.70932168+10.15657639*I
7.899496715+.5339720053*I

expr := sqrt(8)*sqrt(2+I-17/(3-7*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr);evalf(simplify(expr));

6.675262776+5.334495264*I
4.149018940+.2804558370*I

expr := sqrt(3)*sqrt(2+I-17/(3-7*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

4.087746927+3.266697859*I
2.540744835+.1717434241*I

expr := sqrt(2+I-17/(3-7*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

2.360061788+1.886028888*I
1.466899714+.9915611210e-1*I

expr := sqrt(2+I-7/(3-7*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

2.397443833+1.954283845*I
1.457902582+.2603693280*I

expr := sqrt(2+I-7/(3-7*I)^(3/2)+17*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

1.605887074+.7384964577*I
1.454264995+.2369579674*I

expr := sqrt(2+I-7/(3-I)^(3/2)+17*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

1.258172283+.8432721708*I
.9736619297+.2255807954*I

expr := sqrt(2-7/(3-I)^(3/2)+17*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

1.070701246+.5239385632*I
.9887056974-.2835632162*I

expr := sqrt(2-1/(3-I)^(3/2)+17*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

1.457634607+.5547172622*I
1.357501883-.2413783869e-1*I

expr := sqrt(2-1/(1-I)^(3/2)+17*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

1.385395901+.4151662476*I
1.345850725-.1977727670*I

expr := sqrt(2-1/(1-I)^(3/2)+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

1.341273943-.1675126870*I
1.346804173-.2035716309*I

expr := sqrt(1-1/(1-I)^(3/2)+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.9119512444-.2463732612*I
.9272868784-.2956702271*I

expr := sqrt(1-1/(1+I)^(3/2)+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.9431118647+.3442451174*I
.9275992701+.2966485030*I

expr := sqrt(1+1/(1+I)^(3/2)+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

1.125132094-.1996924656*I
1.134011954-.2417709275*I

expr := sqrt(1+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

1.000498272+.4996572969e-1*I
.9999926267+.4999099490e-3*I

expr := sqrt(1+I/(100-I)^(3/2)):
evalf(expr,30); evalf(simplify(expr),30);

1.00049827229562744544995570763+.499657296914860586609692818080e-1*I
.999992626021405252853971985591+.499909948628481845881797005918e-3*I

expr := sqrt(1/(1+I)^(3/2)+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.6037622114-.3721339260*I
.6407823963-.4278693105*I

expr := sqrt(1/(1+I)^(3/2)+1/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.6949131925-.3941803677*I
.6416844166-.4280352181*I

expr := sqrt(1/(1+I)^(3/2)+1/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

.6949131925-.3941803677*I
.6416844166-.4280352181*I

expr := sqrt(1/(1+I)^(3/2)+(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

3.199861153-.1092770355*I
31.62673671-.2458268876*I

expr := sqrt((1+I)^(3/2)+(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

3.269450548+.2146803153*I
31.63307235-.2125352919*I

expr := sqrt(I^(3/2)+(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

3.049731243+.9133692640e-1*I
31.61180952-.2260698760*I

expr := sqrt(I^(1/2)+(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

3.273220722+.8510060939e-1*I
31.63416891-.2259100874*I

expr := sqrt(1+(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

3.316645348-.2261330490e-1*I
31.63887947-.2370511022*I

expr := sqrt((100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));

3.162307306-.2371695893e-1*I
31.62307306-.2371695893*I


expr := sqrt((10^(10^2)+I)^(3/2)):  evalf(expr - simplify(expr));

-.1000000000e76-.7500000000e-25*I


expr := sqrt((100+I)^(5/2)):  evalf(expr - simplify(expr));

-313.0605968-3.913330834*I


expr := sqrt((1+100*I)^(5/2)):  evalf(expr - simplify(expr));

-116.1876574+290.7278447*I


expr := ((1+100*I)^(3/2))^(1/3):  evalf(expr - simplify(expr));

-5.575459692-5.519983861*I


expr := ((100+I)^(3/2))^(1/3):  evalf(expr-simplify(expr));

-7.845663381-.3922733623e-1*I


expr := ((100+I)^(5/2))^(1/4):  evalf(expr-simplify(expr));

-16.00470224-.1000273572*I


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