Greetings to all. I will keep this brief and to the point. I would like to point out a certain deficit in the integral transform package. I have recently been calculating some Mellin transforms at this link and the base functions are of the following type.
g := (p, q) -> 1/(x+p)/(x+(p*q-1)/q);
Now to see the deficit here are some Mellin transforms that I suggest you calculate using the above mentioned package.
mellin(g(3, 2), x, s);
mellin(g(3, 3), x, s);
1/2 1/2 (s/2 - 3/4) 17 8
Pi 3 8 Beta(s, 2 - s) LegendreP(s - 3/2, -1/2, -------)
Maple does not succeed here and produces products of beta function terms and Legendre polynomials that obscure the nature of the solution, namely where the poles are and what the corresponding residues are. As you can see at the above post the answer is very simple and elementary, consisting only of a sine term and some exponentials, where the poles are perfectly obvious and the residues can be calculated trivially with pen and paper. The simplify command did not improve matters.
I hope in bringing this to your attention I can help make Maple a better product.
This issue is with Maple 15 (X86 64 LINUX).
Regards, Marko Riedel.