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Accelerating indefinite hypergeometric summation algorithms

Published: 16 February 2019 Publication History

Abstract

Let K be a field of characteristic zero, x an independent variable, E the shift operator with respect to x, i.e., Ef(x) = f(x + 1) for an arbitrary f(x). Recall that a nonzero expression F(x) is called a hypergeometric term over K if there exists a rational function r(x) ∈ K(x) such that F(x + 1)/F(x) = r(x). Usually r(x) is called the rational certificate of F(x). The problem of indefinite hypergeometric summation (anti-differencing) is: given a hypergeometric term F(x), find a hypergeometric term G(x) which satisfies the first order linear difference equation
(E − 1)G(x) = F(x). (1)
If found, write Σx F(x) = G(x) + c, where c is an arbitrary constant.

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Cited By

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  • (2023)On the Structure of Solutions to the Key Gosper Equation in Problems of Symbolic SummationЖурнал вычислительной математики и математической физики10.31857/S004446692301015563:1(43-50)Online publication date: 1-Jan-2023
  • (2023)On the Structure of Solutions to the Key Gosper Equation in Problems of Symbolic SummationComputational Mathematics and Mathematical Physics10.1134/S096554252301015363:1(40-47)Online publication date: 8-Apr-2023

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Published In

cover image ACM Communications in Computer Algebra
ACM Communications in Computer Algebra  Volume 52, Issue 3
September 2018
67 pages
ISSN:1932-2232
EISSN:1932-2240
DOI:10.1145/3313880
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 16 February 2019
Published in SIGSAM-CCA Volume 52, Issue 3

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View all
  • (2023)On the Structure of Solutions to the Key Gosper Equation in Problems of Symbolic SummationЖурнал вычислительной математики и математической физики10.31857/S004446692301015563:1(43-50)Online publication date: 1-Jan-2023
  • (2023)On the Structure of Solutions to the Key Gosper Equation in Problems of Symbolic SummationComputational Mathematics and Mathematical Physics10.1134/S096554252301015363:1(40-47)Online publication date: 8-Apr-2023

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