Special Function solutions to linear ODEs and new facilities in Maple 9h2>

Edgardo Cheb-Terrab, MITACS - CECM, Simon Fraser University and Maplesoft



The computation of special function solutions for linear ODEs in the Maple
system is performed using four different algorithms, all based on the
formulation of increasingly difficult "equivalence problems".

In this talk the first of these algorithms is described, to resolve (when a
solution exists) the equivalence problem between an arbitrary linear ODE and
any of the 2F1, 1F1 or 0F1 hypergeometric equations, by means of
transformations of the form

                              n
                           p x  + q
                      x -> --------,    y(x) -> P(x) y(x)
                              n
                           r x  + s

where {p, q, r, s, n} are arbitrary constants, and P(x) is an arbitrary function.

The second half of the talk consists of a review of valuable new
functionality introduced in the new Maple release, Maple 9.