We introduce a technique for determining infinite series identities through something of a combination of the modified Abel lemma on summation by parts and a method of undetermined coefficients. We succeed in applying our technique in our proving a nontrivial variant of Gauss’ hypergeometric identity, giving us an evaluation for a family of 3F2(1) -series with three free parameters, and to establish a 3F2(−1)-variant of Kummer’s hypergeometric identity. Also, we apply the technique upon which this article is based to formulate a new and simplified proof of a remarkable series evaluation recently derived by Cantarini via the generalized Clebsch–Gordan integral

A series evaluation technique based on a modified Abel lemma

Cantarini M.
2022

Abstract

We introduce a technique for determining infinite series identities through something of a combination of the modified Abel lemma on summation by parts and a method of undetermined coefficients. We succeed in applying our technique in our proving a nontrivial variant of Gauss’ hypergeometric identity, giving us an evaluation for a family of 3F2(1) -series with three free parameters, and to establish a 3F2(−1)-variant of Kummer’s hypergeometric identity. Also, we apply the technique upon which this article is based to formulate a new and simplified proof of a remarkable series evaluation recently derived by Cantarini via the generalized Clebsch–Gordan integral
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1534296
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