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 \(_4F_3\) 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 \(_4F_3 (1)\), whose further special cases are derived to give thirty two known summation formulas for the terminating \(_4F_3 (1)\). 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.