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Identities for Catalan’s Constant Arising from Integrals Depending on a Parameter

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Abstract

In this paper we provide some relationships between Catalan’s constant and the 3F2 and 4F3 hypergeometric functions, deriving them from some parametric integrals. In particular, using the complete elliptic integral of the first kind, we found an alternative proof of a result of Ramanujan for 3F2, a second identity related to 4F3 and using the complete elliptic integral of the second kind we obtain an identity by Adamchik.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. Free University of Bozen, Bressanone Campus, Viale Ratisbona 16, 39042, Bressanone, BZ, Italy

    Federica Ferretti

  2. Dipartimento di Matematica “G. Castelnuovo”, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185, Roma, Italy

    Alessandro Gambini

  3. Dipartimento di Scienze Statistiche, Università di Bologna, Via delle Belle Arti 41, 40126, Bologna, Italy

    Daniele Ritelli

Authors
  1. Federica Ferretti
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  2. Alessandro Gambini
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  3. Daniele Ritelli
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Corresponding author

Correspondence to Alessandro Gambini.

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Supported by a RFO 2015–2016 (Panel 13)

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Ferretti, F., Gambini, A. & Ritelli, D. Identities for Catalan’s Constant Arising from Integrals Depending on a Parameter. Acta. Math. Sin.-English Ser. 36, 1083–1093 (2020). https://doi.org/10.1007/s10114-020-9451-9

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  • DOI: https://doi.org/10.1007/s10114-020-9451-9

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