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September 2020 Summation identities and transformations for hypergeometric series -- II
Rupam Barman, Neelam Saikia
Funct. Approx. Comment. Math. 63(1): 7-42 (September 2020). DOI: 10.7169/facm/1812

Abstract

McCarthy defined a function in terms of quotients of the $p$-adic gamma functions which can best be described as an analogue of hypergeometric series in the $p$-adic setting. We find six transformations and three summation identities for the McCarthy's $p$-adic hypergeometric series by evaluating certain Gauss sums. We also find a transformation and two summation identities for the Greene's finite field hypergeometric series. Finally, we obtain some special values of the Greene's finite field hypergeometric series as an application of our main results.

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Rupam Barman. Neelam Saikia. "Summation identities and transformations for hypergeometric series -- II." Funct. Approx. Comment. Math. 63 (1) 7 - 42, September 2020. https://doi.org/10.7169/facm/1812

Information

Published: September 2020
First available in Project Euclid: 9 November 2019

MathSciNet: MR4149509
Digital Object Identifier: 10.7169/facm/1812

Subjects:
Primary: 11T24, 33E50
Secondary: 11S80, 33C99

Rights: Copyright © 2020 Adam Mickiewicz University

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Vol.63 • No. 1 • September 2020
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