Applications of a Hypergeometric Identity and Ramanujan-like Series.

The aim of this work is to present an interesting identity relating generalized hypergeometric functions. It allows us to prove many generalizations of recent results, and also to evaluate the sum of several families of Ramanujan-type series for 1 / π , 2 / π and 3 / π . Also, several families of series involving the central binomial coefficients and Harmonic numbers are evaluated. In particular, an explicit evaluation of the series ∑ n = 0 ∞ 4 - 3 n 4 n 2 n C n + m where C n is the nth Catalan number is presented, and a conjectured expression of the sum of this series given in a recent work by Seán M. Stewart is proved to be true. [ABSTRACT FROM AUTHOR]