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Infinite Series Formulae Related to Gauss and Bailey \(_2F_1(\frac{1}{2})\)-Sums

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Abstract

The unified Ω-series of the Gauss and Bailey \(_2F_1(\frac{1}{2})\)-sums will be investigated by utilizing asymptotic methods and the modified Abel lemma on summation by parts. Several remarkable transformation theorems for the Ω-series will be proved whose particular cases turn out to be strange evaluations of nonterminating hypergeometric series and infinite series identities of Ramanujan-type, including a couple of beautiful expressions for π and the Catalan constant discovered by Guillera (2008).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001, China

    Wenchang Chu

  2. Department of Mathematics and Physics, ]University of Salento, P. O. Box 193, 73100, Lecce, Italy

    Wenchang Chu

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  1. Wenchang Chu
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Correspondence to Wenchang Chu.

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Chu, W. Infinite Series Formulae Related to Gauss and Bailey \(_2F_1(\frac{1}{2})\)-Sums. Acta Math Sci 40, 293–315 (2020). https://doi.org/10.1007/s10473-020-0201-y

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  • DOI: https://doi.org/10.1007/s10473-020-0201-y

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