Yabu's formulae for hypergeometric $ _3F_2 $-series through Whipple's quadratic transformations

Marta Na Chen; Wenchang Chu; Marta Na Chen; Wenchang Chu

doi:10.3934/math.20241060

AIMS Mathematics

2024, Volume 9, Issue 8: 21799-21815. doi: 10.3934/math.20241060

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Yabu's formulae for hypergeometric $ _3F_2 $-series through Whipple's quadratic transformations

Marta Na Chen ¹,
Wenchang Chu ^{2
,
,}

1.
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, China; chennamarta@zknu.edu.cn
2.
Via Dalmazio Birago 9/E, Lecce 73100, Italy

Received: 22 May 2024 Revised: 28 June 2024 Accepted: 02 July 2024 Published: 09 July 2024
MSC : Primary 33C20, Secondary 33C90

By means of Whipple's quadratic transformations, two classes of hypergeometric $ _3F_2 $-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.
- hypergeometric series,
- Whipple's quadratic transformations,
- the Lerch transcendent function
Citation: Marta Na Chen, Wenchang Chu. Yabu's formulae for hypergeometric $ _3F_2 $-series through Whipple's quadratic transformations[J]. AIMS Mathematics, 2024, 9(8): 21799-21815. doi: 10.3934/math.20241060

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Abstract

By means of Whipple's quadratic transformations, two classes of hypergeometric $ _3F_2 $-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.

References

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