Generalization of two theorems due to Ramanujan

The aim in this paper is to provide generalizations of two interesting entries in Ramanujan's notebooks that relate sums involving the derivatives of a function φ(t) evaluated at 0 and 1. The generalizations obtained are derived with the help of expressions for the Gauss hypergeometric function ₂ F ₁(−n, a; 2a+j; 2) for non-negative integer n and j=0,±1, …,±5 given very recently by Kim et al. [Generalizations of Kummer's second theorem with applications, Comput. Math. Math. Phys. 50(3) (2010), pp. 387–402] and extension of Gauss’ summation theorem available in the literature. Several special cases that are closely related to Ramanujan's results are also given.