English

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 k=0akzk\sum\limits_{k=0}^{\infty}a_{k}z^{k} 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}.

Keywords

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}
}
R2 v1 2026-07-22T17:54:49.052Z