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.
Identities for Catalan’s constant arising from integrals depending on a parameter / Ferretti, F.; Gambini, A.; Ritelli, D.. - In: ACTA MATHEMATICA SINICA. - ISSN 1439-8516. - 36:10(2020), pp. 1083-1093. [10.1007/s10114-020-9451-9]
Identities for Catalan’s constant arising from integrals depending on a parameter
Gambini A.
;
2020
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.| File | Dimensione | Formato | |
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