RISC RISC Research Institute for Symbolic Computation  
  • @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}