The aim of this research paper is to obtain explicit expressions of 2F1 a, b1 2 (a + b ± ` + 1) ; 1 + x 2 in the most general case for any ∂ = 0, 1, 2, . . . . For ` = 0, we have the well known, interesting and useful formula due to Kummer which was proved independently by Ramanujan. The results presented here are obtained with the help of known generalizations of Gauss’s second summation theorem for the series 2F1( 12 ), which were given earlier by Rakha and Rathie [Integral Transforms Spec. Func. 22 (11) (2011), 823–840]. The results are further utilized to obtain new hypergeometric identities by using beta integral method developed by Krattenthaler & Rao [J. Comput. Appl. Math. 160 (2003), 159–173]. Several interesting results due to Ramanujan, Choi, et. al. and Krattenthaler & Rao follow special cases of our main findings