2020/05/11 by С. А. Абрамов, Sergei A. Abramov, Manuel Bronstein +6 · 5 citations
Computer Science · Mathematics · #Algebra over a field #Applied mathematics #Class (philosophy) #Combinatorics #Computer science #FOS: Computer and information sciences #Field (mathematics) #Homogeneous #Hypergeometric distribution #Hypergeometric function #Mathematics #Parameterized complexity #Polynomial and algebraic computation #Pure mathematics #Symbolic Computation (cs.SC) #Tower #cs.SC
paper · pdf · doi:10.48550/arxiv.2005.04944
published in arXiv (Cornell University) (Cornell University) · Various typos have been removed and the presentation has been improved
openalex publication_date 2020/05/11 · arxiv created 2021/01/25 · arxiv updated 2021/01/27 · openalex created_date 2022/07/26 · openalex updated_date 2026/08/05
We present a complete algorithm that computes all hypergeometric solutions of homogeneous linear difference equations and rational solutions of parameterized linear difference equations in the setting of ΠΣ^*-fields. More generally, we provide a flexible framework for a big class of difference fields that is built by a tower of ΠΣ^*-field extensions over a difference field that satisfies certain algorithmic properties. As a consequence one can compute all solutions in terms of indefinite nested sums and products that arise within the components of a parameterized linear difference equation, and one can find all hypergeometric solutions that are defined over the arising sums and products of a homogeneous linear difference equation.