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

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).