A NOTE ON A NEW AND GENERAL SUMMATION FORMULA FOR THE GENERALIZED HYPERGEOMETRIC SERIES $_4F_3(1)$

The main purpose of this note is to demonstrate how one can obtain a new and general summation formula for the generalized hypergeometric series $_4F_3(1)$. This is achieved by employing two generalizations of the Gauss's second summation theorems obtained earlier by Rakha and Rathie in an identity due to Bailey. Several results obtained earlier by Ali et al. follow special cases of our main findings.