@**article**{RISC2393,author = {R. Pirastu and V. Strehl},

title = {{Rational Summation and Gosper-Petkovsek Representation}},

language = {english},

abstract = {{\em Indefinite} summation essentially deals with the problem
of inverting the difference operator
$\Delta \,:\,f(X) \rightarrow f(X+1) - f(X)$.
In the case of rational functions over a field $k$ we consider
the following version of the problem
\begin{itemize}
\item
given $\alpha \in k(X)$, determine $\beta, \gamma \in k(X)$ such that
$\alpha = \Delta\,\beta + \gamma$, where $\gamma$ is as ``small''
as possible (in a suitable sense).
\end{itemize}
In particular, we address the question
\begin{itemize}
\item
what can be said about the denominators of a solution $(\beta, \gamma)$
by looking at the denominator of $\alpha$ only ?
\end{itemize}
An ``optimal'' answer to this question can be given in terms of the
Gosper-Petkov\v{s}ek representation for rational functions, which was
originally invented for the purpose of indefinite hypergeometric
summation. %[{ Gosper (1978)}, { Pet\-kov\-\v{s}ek} (1992)].
This information can be used to construct a simple new algorithm
for the rational summation problem.},

journal = {J. Symbolic Comput.},

volume = {20},

pages = {617--635},

isbn_issn = {ISSN 0747-7171},

year = {1995},

refereed = {yes},

length = {19}

}