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/pi, root 2/pi and root 3/pi. Also, several families of series involving the central binomial coefficients and Harmonic numbers are evaluated. In particular, an explicit evaluation of the series Sigma(infinity)(n=0) 4(-3n) (4n 2n) Cn+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 Sean M. Stewart is proved to be true.