Turkish Journal of Mathematics
Abstract
Explicit expressions for the hypergeometric series $_2F_1(-n, a; 2a\pm j;2)$ and $_2F_1(-n, a; -2n \pm j;2)$ for positive integer $n$ and arbitrary integer $j$ are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for $ j \leq 5$ derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating $_3F_2(2)$ series and the confluent hypergeometric function $_1F_1(x)$.
DOI
10.3906/mat-1804-67
Keywords
Terminating hypergeometric series, generalized Kummer's second and third summation theorems
First Page
2563
Last Page
2575
Recommended Citation
KIM, Y. S, RATHIE, A, & PARIS, R. B (2018). Evaluations of some terminating hypergeometric $_2F_1(2)$ series with applications. Turkish Journal of Mathematics 42 (5): 2563-2575. https://doi.org/10.3906/mat-1804-67
