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