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Turkish Journal of Mathematics

DOI

10.55730/1300-0098.3177

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 ${}_{3}F_{2}(1)$-series with three free parameters, and to establish a ${}_{3}F_{2}(-1)$-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.

First Page

1520

Last Page

1537

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Mathematics Commons

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