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Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients

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Abstract

The Gauss summation theorem and an extended \(_3F_2\)-series of Watson and Whipple type are examined by means of power series expansions. Numerous Ramanujan-like series involving harmonic numbers and squared central binomial coefficients are evaluated in closed forms. Several remarkable identities discovered by Campbell (Ramanujan J 46(2):373–387, 2018) are included as particular cases.

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Acknowledgements

The authors are sincerely grateful to an anonymous referee for the careful reading and valuable comments.

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Authors and Affiliations

  1. School of Science, Dalian Jiaotong University, Dalian, 116028, People’s Republic of China

    Xiaoyuan Wang

  2. Department of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001, People’s Republic of China

    Wenchang Chu

  3. Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, P. O. Box 193, Arnesano, 73100, Lecce, Italy

    Wenchang Chu

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  1. Xiaoyuan Wang
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Correspondence to Wenchang Chu.

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Wang, X., Chu, W. Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients. Ramanujan J 52, 641–668 (2020). https://doi.org/10.1007/s11139-019-00140-5

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