$$\Gamma $$-evaluations of hypergeometric series-Reference-Cited by-同舟云学术

$$\Gamma $$-evaluations of hypergeometric series

Published:2022-05-19 Issue:3 Volume:58 Page:677-699
ISSN:1382-4090
Container-title:The Ramanujan Journal
language:en
Short-container-title:Ramanujan J

Author:

Beukers Frits^ORCID,Forsgård Jens

Abstract

AbstractIn this paper we explore special values of Gaussian hypergeometric functions in terms of products of Euler

$$\Gamma $$

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.

Funder

NWO

Publisher

Springer Science and Business Media LLC

Subject

Algebra and Number Theory

Link

https://link.springer.com/content/pdf/10.1007/s11139-022-00566-4.pdf

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4. Beukers, F.: Hypergeometric functions, from Riemann till present. In: Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds and Picard-Fuchs Equations (eds. Lizhen Ji, Shing-Tung Yau) Advanced Lectures in Mathematics, pp. 1–19. Higher Education Press, Beijing (2018)

5. Beukers, F.: Algebraic values of G-functions. J. für Reine Angew. Math. 434, 45–65 (1993)

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