A Non-Holonomic Systems Approach to Special Function Identities

Frederic Chyzak; Manuel Kauers; Bruno Salvy

doi:10.1145/1576702.1576720

A Non-Holonomic Systems Approach to Special Function Identities

Frederic Chyzak
, Manuel Kauers
, Bruno Salvy

Research Institute for Symbolic Computation

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

Abstract

We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma function or polylogarithms, which are not covered by the holonomic framework. The basic idea is to take into account the dimension of appropriate ideals in Ore algebras. This unifies several earlier extensions and provides algorithms for summation and integration in classes that had not been accessible to computer algebra before.

Original language	English
Title of host publication	ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation
Editors	John May
Pages	111-118
Number of pages	8
DOIs	https://doi.org/10.1145/1576702.1576720
Publication status	Published - 2009

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

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10.1145/1576702.1576720

Cite this

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title = "A Non-Holonomic Systems Approach to Special Function Identities",

abstract = "We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma function or polylogarithms, which are not covered by the holonomic framework. The basic idea is to take into account the dimension of appropriate ideals in Ore algebras. This unifies several earlier extensions and provides algorithms for summation and integration in classes that had not been accessible to computer algebra before.",

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N2 - We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma function or polylogarithms, which are not covered by the holonomic framework. The basic idea is to take into account the dimension of appropriate ideals in Ore algebras. This unifies several earlier extensions and provides algorithms for summation and integration in classes that had not been accessible to computer algebra before.

AB - We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma function or polylogarithms, which are not covered by the holonomic framework. The basic idea is to take into account the dimension of appropriate ideals in Ore algebras. This unifies several earlier extensions and provides algorithms for summation and integration in classes that had not been accessible to computer algebra before.

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U2 - 10.1145/1576702.1576720

DO - 10.1145/1576702.1576720

M3 - Conference proceedings

SN - 978-1-60558-609-0

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EP - 118

BT - ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation

A2 - John May, null

ER -

A Non-Holonomic Systems Approach to Special Function Identities

Abstract

Fields of science

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