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