On rational and hypergeometric solutions of linear ordinary difference equations in ΠΣ⁎-field extensions. (November 2021)

• Record Type: Journal Article
• Authors: Abramov, Sergei A.; Bronstein, Manuel; Petkovšek, Marko; Schneider, Carsten
• Is Part Of: Journal of symbolic computation. Volume 107(2021)
• Page Start: 23
• Page End: 66
• Publication Date: 2021-11
• Subjects: 12H10 -- 39A06 -- 68W30; Difference fields -- Rational solutions -- Hypergeometric solutions; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2021.01.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: 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 Π Σ ⁎ -fields. More generally, we provide a flexible framework for a big class of difference fields that are built by a tower of Π Σ ⁎ -field extensions over a difference field that enjoys 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 of a homogeneous linear difference equation that are defined over the arising sums and products.