Γ -evaluations of hypergeometric series

Frits Beukers; Jens Forsgård

doi:10.1007/s11139-022-00566-4

Γ -evaluations of hypergeometric series

Frits Beukers^*, Jens Forsgård

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

In this paper we explore special values of Gaussian hypergeometric functions in terms of products of Euler Γ -functions and exponential functions of linear functions of the hypergeometric parameters. They include some classical evaluations, but the main inspiration is from the contiguity method recently applied by Akihito Ebisu.

Original language	English
Pages (from-to)	677-699
Number of pages	23
Journal	Ramanujan Journal
Volume	58
Issue number	3
DOIs	https://doi.org/10.1007/s11139-022-00566-4
Publication status	Published - Jul 2022

Keywords

Gamma function
Gauss hypergeometric function
Special values

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title = "Γ -evaluations of hypergeometric series",

abstract = "In this paper we explore special values of Gaussian hypergeometric functions in terms of products of Euler Γ -functions and exponential functions of linear functions of the hypergeometric parameters. They include some classical evaluations, but the main inspiration is from the contiguity method recently applied by Akihito Ebisu.",

keywords = "Gamma function, Gauss hypergeometric function, Special values",

author = "Frits Beukers and Jens Forsg{\aa}rd",

note = "Funding Information: This work was supported by the Netherlands Organisation for Scientific Research (NWO), Grant TOP1EW.15.313. Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2022",

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AU - Beukers, Frits

AU - Forsgård, Jens

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AB - In this paper we explore special values of Gaussian hypergeometric functions in terms of products of Euler Γ -functions and exponential functions of linear functions of the hypergeometric parameters. They include some classical evaluations, but the main inspiration is from the contiguity method recently applied by Akihito Ebisu.

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KW - Gauss hypergeometric function

KW - Special values

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EP - 699

JO - Ramanujan Journal

JF - Ramanujan Journal

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Γ -evaluations of hypergeometric series

Abstract

Keywords

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