Order-Degree Curves for Hypergeometric Creative Telescoping

Shaoshi Chen; Manuel Kauers

doi:10.48550/arXiv.1201.1982

Order-Degree Curves for Hypergeometric Creative Telescoping

Shaoshi Chen, Manuel Kauers

Research Institute for Symbolic Computation

Research output: Working paper and reports › Preprint

Abstract

Creative telescoping applied to a bivariate proper hypergeometric term produces linear recurrence operators with polynomial coefficients, called telescopers. We provide bounds for the degrees of the polynomials appearing in these operators. Our bounds are expressed as curves in the (r,d)-plane which assign to every order r a bound on the degree d of the telescopers. These curves are hyperbolas, which reflect the phenomenon that higher order telescopers tend to have lower degree, and vice versa.

Original language	English
Place of Publication	Hagenberg
Publisher	RISC JKU
Number of pages	8
DOIs	https://doi.org/10.48550/arXiv.1201.1982
Publication status	Published - 2012

Publication series

Name	arXiv.org

Fields of science

101001 Algebra
101002 Analysis
101 Mathematics
102 Computer Sciences
102011 Formal languages
101009 Geometry
101013 Mathematical logic
101020 Technical mathematics
101025 Number theory
101012 Combinatorics
101005 Computer algebra
101006 Differential geometry
101003 Applied geometry
102025 Distributed systems

JKU Focus areas

Computation in Informatics and Mathematics

Access to Document

10.48550/arXiv.1201.1982

Cite this

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AB - Creative telescoping applied to a bivariate proper hypergeometric term produces linear recurrence operators with polynomial coefficients, called telescopers. We provide bounds for the degrees of the polynomials appearing in these operators. Our bounds are expressed as curves in the (r,d)-plane which assign to every order r a bound on the degree d of the telescopers. These curves are hyperbolas, which reflect the phenomenon that higher order telescopers tend to have lower degree, and vice versa.

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