Evaluations of some terminating hypergeometric $_2F_1(2)$ series with applications

Authors : Yong Sup KIM, Arjunkumar RATHIE, Richard B. PARIS

Pages : 2563-2575

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Explicit expressions for the hypergeometric series $_2F_1insert ignore into journalissuearticles values(-n, a; 2a\pm j;2);$ and $_2F_1insert ignore into journalissuearticles values(-n, a; -2n \pm j;2);$ 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 $_3F_2insert ignore into journalissuearticles values(2);$ series and the confluent hypergeometric function $_1F_1insert ignore into journalissuearticles values(x);$.
Keywords : Terminating hypergeometric series, generalized Kummer`s second and third summation theorems