I just had occasion to try hgfred. There are errors in simplification in
this program that allow it to generate
subexpressions like (1- -x) or even (1 - -36). Someone is producing
expressions with incorrect ((mtimes simp)..)
headers. Unfortunately I didn't catch the examples before my system
crashed. But there are other probs.
as an example, consider
i3(m,k,a,x):=(x^(1 + m)*(a^2 + x^2)^k*hgfred([(1 + m)/2, -k],
[1 + (1 + m)/2], -(x^2/a^2))/((1 + m)*(1 + x^2/a^2)^k));
i3(m,k,a,x)
should, I think, be the integral of x^m*(x^2+a^2)^k.
The following example (and many others) give odd messages like
SIMP2F1-WILL-CONTINUE-IN
i3(2,3/2,a,x)
i3(0,1,a,x) [also says FAIL-1-IN-C-1-CASE]
i3(1,1/2,a,x) [gives "non-variable 2nd argument to diff, -x^2/a^2]
also some of the answers come out in terms of jacobi_p functions, but
diff does not know about them.
Thanks for help
RJF