On the application of a hypergeometric identity to generate generalized hypergeometric reduction formulas

We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct new summation formulas involving finite sums involving the psi function, or a recursive formula for the Bateman’s G function are derived. Finally, all the results have been numerically checked with MATHEMATICA.