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On rational and hypergeometric solutions of linear ordinary difference equations in ΠΣ⁎-field extensions
- Source :
- Journal of Symbolic Computation. 107:23-66
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
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.
- Subjects :
- Pure mathematics
Class (set theory)
Algebra and Number Theory
010102 general mathematics
Parameterized complexity
Field (mathematics)
010103 numerical & computational mathematics
01 natural sciences
Tower (mathematics)
Hypergeometric distribution
Computational Mathematics
Field extension
Homogeneous
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
0101 mathematics
Linear difference equation
Mathematics
Subjects
Details
- ISSN :
- 07477171
- Volume :
- 107
- Database :
- OpenAIRE
- Journal :
- Journal of Symbolic Computation
- Accession number :
- edsair.doi...........77d6a8f1456bdd5bbd657fad3f2a8fa3