Generalizations of Certain Summation Formulas Involving the Generalized Hypergeometric Function via Eslahchi and Masjed-Jamei

Abstract

Classical summation theorems for generalized hypergeometric series constitute an important tool in the study of special functions. Motivated by earlier generalizations of these theorems, this paper derives several new summation formulas for generalized hypergeometric functions by employing the generalized classical summation theorems of Lavoie et al. within a well-known hypergeometric identity. The proposed formulas extend previously reported results, including those of Eslahchi and Masjed-Jamei, which arise as special cases of the present work. The obtained identities provide a unified framework for deriving summation formulas and may be useful in further investigations involving generalized hypergeometric functions and related identities.