On rational and hypergeometric solutions of linear ordinary difference equations in \(\Pi\Sigma^\ast\)-field extensions
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Publication:2029003
DOI10.1016/j.jsc.2021.01.002zbMath1483.12005arXiv2005.04944OpenAlexW3126493290MaRDI QIDQ2029003
Publication date: 3 June 2021
Published in: Journal of Symbolic Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.04944
Symbolic computation and algebraic computation (68W30) Difference algebra (12H10) Linear difference equations (39A06)
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Cites Work
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- A difference ring theory for symbolic summation
- The two-mass contribution to the three-loop gluonic operator matrix element \(A_{g g, Q}^{(3)}\)
- Problems of computer algebra involved in the search for polynomial solutions of linear differential and difference equations
- Degree bounds to find polynomial solutions of parameterized linear difference equations in \(\Pi\Sigma\)-fields
- A refined difference field theory for symbolic summation
- Polynomial ring automorphisms, rational \((w,\sigma )\)-canonical forms, and the assignment problem
- Theory of summation in finite terms
- A holonomic systems approach to special functions identities
- The method of creative telescoping
- Liouvillian solutions of linear differential equations with Liouvillian coefficients
- Hypergeometric solutions of linear recurrences with polynomial coefficients
- Non-commutative elimination in Ore algebras proves multivariate identities
- Solving difference equations in finite terms
- Finite singularities and hypergeometric solutions of linear recurrence equations
- Symbolic integration. I: Transcendental functions
- An introduction to pseudo-linear algebra
- Galois theory of difference equations
- \(q\)-hypergeometric solutions of \(q\)-difference equations
- On solutions of linear ordinary difference equations in their coefficient field
- Summation theory. II: Characterizations of \(R {\Pi}{\Sigma}^{\ast}\)-extensions and algorithmic aspects
- Refined holonomic summation algorithms in particle physics
- Denominator bounds for systems of recurrence equations using \(\Pi\Sigma\)-extensions
- Representing \((q-)\)hypergeometric products and mixed versions in difference rings
- Product representations in \(\Pi\Sigma\)-fields
- Theory of non-commutative polynomials
- \( m\)-fold hypergeometric solutions of linear recurrence equations revisited
- Multibasic and mixed hypergeometric Gosper-type algorithms
- An extension of Zeilberger's fast algorithm to general holonomic functions
- Minimal representations and algebraic relations for single nested products
- In memory of Manuel Bronstein
- A new Sigma approach to multi-summation
- Indefinite summation with unspecified summands
- Computing hypergeometric solutions of second order linear differential equations using quotients of formal solutions and integral bases
- Symbolic summation assists combinatorics
- Fast Algorithms for Refined Parameterized Telescoping in Difference Fields
- Hypergeometric dispersion and the orbit problem
- An Extension of Liouville’s Theorem on Integration in Finite Terms
- Summation in Finite Terms
- Creative Telescoping for Holonomic Functions
- Solving Linear Recurrence Equations with Polynomial Coefficients
- Simplifying Multiple Sums in Difference Fields
- Solving parameterized linear difference equations in terms of indefinite nested sums and products
- The Problem of Integration in Finite Terms
- On the summation of rational functions
- Rational solutions of linear differential and difference equations with polynomial coefficients
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