7.142 Bug report for int in Maple V.5 and Maple 6 (20.8.99)

7.142.1 Ferdinand Gleisberg

The solution of the following Integral

> assume(a>0); 
> w:=Int(x*exp(-a/x)/(1+x^(3/2))^2,x=0..infinity); 
 
                               infinity          a~ 
                              /         x exp(- ----) 
                             |                   x 
                       w :=  |          ------------- dx 
                             |                 3/2 2 
                             |           (1 + x   ) 
                            / 
                              0 
 
> w1:=value(w); 
 
                    / 
                    |      3                                             3 
                1/2 |    Pi  hypergeom([5/6], [-1/6, 1/3, 2/3], - 1/27 a~ ) 
w1 := - 1/9 a~ 3    |4/3 -------------------------------------------------- 
                    |                            a~ 
                    | 
                    \ 
 
             3                                            3          2     1/2 
     - 4/3 Pi  hypergeom([7/6], [1/6, 2/3, 4/3], - 1/27 a~ ) - 3/2 Pi  a~ 3 
 
    /infinity 
    | ----- 
    |  \          (2 _k1) 
    |   )     (-1)        (Psi(3/2 + _k1) - Psi(1 + _k1) - Psi(5/3 + _k1) 
    |  / 
    | ----- 
    \_k1 = 0 
 
     + Pi cot(-Pi _k1 + 1/3 Pi) - Psi(4/3 + _k1) - Pi tan(-Pi _k1 + 1/6 Pi) 
 
                                                               (3 _k1) 
     - Psi(1/2 + _k1) + Pi tan(Pi _k1) + 3 ln(a~) - 3 ln(3)) a~ 
 
     (-3 _k1)                                                          (3 _k1) 
    3         sec(-Pi _k1 + 1/6 Pi) csc(-Pi _k1 + 1/3 Pi) sec(Pi _k1) 3 
 
                                \ 
                                | 
                                | 
    (1/2 + _k1)/GAMMA(3 + 3 _k1)| 
                                | 
                                | 
                                / 
 
                                                                        \ 
                                                                        | 
       32   5/2   5/2  1/2                                            3 |   / 
     - -- Pi    a~    3    hypergeom([2], [3/2, 11/6, 13/6], - 1/27 a~ )|  / 
       35                                                               | / 
                                                                        | 
                                                                        / 
 
      2 
    Pi
 

( which Mma is unable to solve at all ! )

> evalf(subs(a=1,w1)); 
                                 -.4502788024 
 
> evalf(subs(a=1,w)); 
                                  .4502788021
 

seems to have a bug in the sign.

It is corrected with Maple 7. (U. Klein)