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Research Article | Open Access

Yabu's formulae for hypergeometric 3F2-series through Whipple's quadratic transformations

Marta Na Chen1, Wenchang Chu2( )
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, China; chennamarta@zknu.edu.cn
Via Dalmazio Birago 9/E, Lecce 73100, Italy
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Abstract

By means of Whipple's quadratic transformations, two classes of hypergeometric 3F2-series are expressed in terms of the Lerch transcendent function. Several difficult series with a free variable are explicitly evaluated in closed form, including Yabu's three remarkable identities.

Keywords

hypergeometric seriesWhipple's quadratic transformationsthe Lerch transcendent function
CLC number: Primary 33C20, Secondary 33C90

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 21799-21815
DOI: 10.3934/math.20241060

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Cite this article:
Chen MN, Chu W. Yabu's formulae for hypergeometric 3F2-series through Whipple's quadratic transformations. AIMS Mathematics, 2024, 9(8): 21799-21815. https://doi.org/10.3934/math.20241060

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Received: 22 May 2024
Revised: 28 June 2024
Accepted: 02 July 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)