- Turkish Journal of Mathematics
- Vol: 42 Issue: 5
- Evaluations of some terminating hypergeometric $_2F_1(2)$ series with applications
Evaluations of some terminating hypergeometric $_2F_1(2)$ series with applications
Authors : Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris
Pages : 2563-2575
View : 7 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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 $_1F_1(x)$.Keywords : Terminating hypergeometric series, generalized Kummer's second and third summation theorems