Turkish Journal of Mathematics
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.
DOI
10.55730/1300-0098.3177
Keywords
Abel lemma, Kummer's identity, closed form, generalized hypergeometric functions
First Page
1520
Last Page
1537
Recommended Citation
CAMPBELL, J. M, & CANTARINI, M (2022). A series evaluation technique based on a modified Abel lemma. Turkish Journal of Mathematics 46 (4): 1520-1537. https://doi.org/10.55730/1300-0098.3177
