A new algorithm for the recursion of multisums with improved universal denominator

Details A new algorithm for the recursion of multisums with improved universal denominator A new algorithm for the recursion of multisums with improved universal denominator

2008-09-26

arxiv.org/abs/0809.4696v3

Mathematics

Combinatorics

12 pages, no figures

Scientific paper

The purpose of the paper is to introduce two new algorithms. The first one computes a linear recursion for proper hypergeometric multisums, by treating one summation variable at a time, and provides rational certificates along the way. A key part in the search of a linear recursion is an improved universal denominator algorithm that constructs all rational solutions $x(n)$ of the equation $$ \frac{a_m(n)}{b_m(n)}x(n+m)+...+\frac{a_0(n)}{b_0(n)}x(n)= c(n),$$ where $a_i(n), b_i(n), c(n)$ are polynomials. Our algorithm improves Abramov's universal denominator.

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