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EVALUATION OF CERTAIN EXOTIC $_3F_2$(1)-SERIES

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  05 September 2022

MARTA NA CHEN Open the ORCID record for MARTA NA CHEN [Opens in a new window]  and
WENCHANG CHU Open the ORCID record for WENCHANG CHU [Opens in a new window]
MARTA NA CHEN
Affiliation:
School of Mathematics and Statistics Zhoukou Normal University Zhoukou, China chennaml@outlook.com
WENCHANG CHU
Affiliation:
Department of Mathematics and Physics University of Salento, Lecce, Italy chu.wenchang@unisalento.it
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Abstract

A class of exotic $_3F_2(1)$-series is examined by integral representations, which enables the authors to present relatively easier proofs for a few remarkable formulae. By means of the linearization method, these $_3F_2(1)$-series are further extended with two integer parameters. A general summation theorem is explicitly established for these extended series, and several sample summation identities are highlighted as consequences.

MSC classification

Primary: 33C20: Generalized hypergeometric series, $_pF_q$
Secondary: 11R33: Integral representations related to algebraic numbers; Galois module structure of rings of integers

Information

Type
Article
Information
Nagoya Mathematical Journal , Volume 249 , March 2023 , pp. 107 - 118
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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