Spaces of functions satisfying simple differential equations
Classical Analysis and ODEs
2009-09-25 v1
Abstract
In \cite{Koe92}--\cite{Koe93c} the first author published an algorithm for the conversion of analytic functions for which derivative rules are given into their representing power series at the origin and vice versa, implementations of which exist in {\sc Mathematica} \cite{Wol}, (s.\ \cite{Koe93c}), {\sc Maple} \cite{Map} (s.\ \cite{GK}) and {\sc Reduce} \cite{Red} (s.\ \cite{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 {\sl simple}.
Cite
@article{arxiv.math/9404222,
title = {Spaces of functions satisfying simple differential equations},
author = {Wolfram Koepf and Dieter Schmersau},
journal= {arXiv preprint arXiv:math/9404222},
year = {2009}
}