Partial denominator bounds for partial linear difference equations
Manuel Kauers,Carsten Schneider +1 more
- 25 Jul 2010
- pp 211-218
TL;DR: A generalization of a well-known denominator bounding technique for univariate equations to PLDEs is able to find all the aperiodic factors of the denominators for a given PLDE.
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Abstract: We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them periodic and aperiodic. The main result is a generalization of a well-known denominator bounding technique for univariate equations to PLDEs. This generalization is able to find all the aperiodic factors of the denominators for a given PLDE.
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Citations
Valuations of rational solutions of linear difference equations at irreducible polynomials
A. Gheffar,S. A. Abramov +1 more
TL;DR: Two algorithms are discussed which, given a linear difference equation with rational function coefficients over a field k of characteristic 0, construct a finite set M of polynomials, irreducible in k[x], such that if the given equation has a solution F(x)@?k( x) and val"p"("x")F(x).
17
A refined denominator bounding algorithm for multivariate linear difference equations
Manuel Kauers,Carsten Schneider +1 more
- 08 Jun 2011
TL;DR: In this article, the polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation, and an algorithm for predicting the aperiodic ones is presented.
13
On rational solutions of linear partial differential or difference equations
TL;DR: It is proved that the problem of recognition of the existence of solutions as rational functions for linear homogeneous partial differential or difference equations with polynomial coefficients is algorithmically undecidable.
11
Hypergeometric structures in Feynman integrals
TL;DR: In this paper , the authors derive new symbolic tools to gain large-scale computer understanding in perturbative Quantum Chromodynamics (QCD) by exploiting the hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies.
9
•Posted Content
A Refined Denominator Bounding Algorithm for Multivariate Linear Difference Equations
Manuel Kauers,Carsten Schneider +1 more
TL;DR: The distinction between periodic and aperiodic factors in the denominator is introduced and an algorithm for predicting the aperiodics ones is given and a refined algorithm is presented which also finds most of the periodic factors.
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