A new algorithm for the recursion of multisums with improved universal denominator
Abstract
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 am(n)bm(n)x(n+m)+...+a0(n)b0(n)x(n)= c(n), where ai(n), bi(n), c(n) are polynomials. Our algorithm improves Abramov's universal denominator.
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