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arXiv · 2005.04672

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

Federica Ferretti·Alessandro Gambini·Daniele Ritelli
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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.

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Federica Ferretti, Alessandro Gambini, Daniele Ritelli. 2020-05-10. Identities for Catalan's constant arising from integrals depending on a parameter. https://arxiv.org/abs/2005.04672

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