2008/09/26 by Stavros Garoufalidis, Xinyu Sun, Garoufalidis, Stavros +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Algebra over a field #Algorithm #Combinatorics #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Computer science #Discrete mathematics #FOS: Mathematics #Hypergeometric function #Key (lock) #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Pure mathematics #Recursion (computer science) #Variable (mathematics) #math.AC #math.CO
paper · pdf · doi:10.48550/arxiv.0809.4696
12 pages, no figures
openalex publication_date 2008/09/26 · arxiv created 2009/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.