Certain new summation formulas for the series 4F3(1) with applications

The main objective of this paper is to provide thirteen (presumably) new summation formulas for the series 4F3 of unit argument expressed in terms of Gamma functions. As special cases of our main results, we also present twenty four summation formulas for the terminating 4F3(1), whose further special cases are derived to give thirty two known summation formulas for the terminating 3F2(1). The results presented here are established with the help of a general result recorded in the book of Prudnikov et al. and the generalization of Watson’s summation theorem obtained earlier by Lavoie et al.