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.
Keywords
Abel lemma, Kummer's identity, closed form, generalized hypergeometric functions
First Page
1520
Last Page
1537
Recommended Citation
CAMPBELL, JOHN MAXWELL and CANTARINI, MARCO
(2022)
"A series evaluation technique based on a modified Abel lemma,"
Turkish Journal of Mathematics: Vol. 46:
No.
4, Article 30.
https://doi.org/10.55730/1300-0098.3177
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss4/30
