Authors have derived a number of interesting reducible cases with the help of recently derived summation theorem of Triple hypergeometric series \(H_A\) and \(H_C\) introduced by H. M. Srivastava. The results derived in this paper are actually generalizations of results established by Rathie and others [Y. S. Kim, A. K. Rathie and J. Choi, Commun. Korean Math. Soc. 18, No. 3, 581–586 (2003; Zbl 1101.33303).