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Explicit expressions for the hypergeometric series 2F1(−n, a; 2a±j; 2) and 2F1(−n, a;−2n±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| ≤ 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 3F2(2) series and the confluent hypergeometric function 1F1(x) .

Evaluations of some terminating hypergeometric 2 F 1 (2) series with applications