Spaces of functions satisfying simple differential equations
Wolfram Koepf, Dieter Schmersau
Abstract
In Koe92--Koe93c the first author published an algorithm for the conversion of analytic functions for which derivative rules are given into their representing power series Σk=0∞akzk at the origin and vice versa, implementations of which exist in Mathematica Wol, (s.\ Koe93c), Maple Map (s.\ GK) and Reduce Red (s.\ Neun). One main part of this procedure is an algorithm to derive a homogeneous linear differential equation with polynomial coefficients for the given function. We call this type of ordinary differential equations simple.
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