Identities for Catalan's constant arising from integrals depending on a parameter

Federica Ferretti; Alessandro Gambini; Daniele Ritelli

Identities for Catalan's constant arising from integrals depending on a parameter

Classical Analysis and ODEs 2020-05-12 v1

Authors: Federica Ferretti , Alessandro Gambini , Daniele Ritelli

Abstract

In this paper we provide some relationships between Catalan's constant and the $_3{\rm F}_2$ and $_4{\rm F}_3$ 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 $_3{\rm F}_2$ , a second identity related to $_4{\rm F}_3$ and using the complete elliptic integral of the second kind we obtain an identity by Adamchik.

Cite

@article{arxiv.2005.04672,
  title  = {Identities for Catalan's constant arising from integrals depending on a parameter},
  author = {Federica Ferretti and Alessandro Gambini and Daniele Ritelli},
  journal= {arXiv preprint arXiv:2005.04672},
  year   = {2020}
}

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10 pages, accepted for publication

Identities for Catalan's constant arising from integrals depending on a parameter

Abstract

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