On Two Summation Formulas for the Generalized Hypergeometric Functions 3F2(1) and 4F3(1) - Atash, Ahmed Ali; Bellehaj, Hussein Saleh (General Letters in Mathematics, 2025)
In this paper, we derive two new summation formulas for the generalized hypergeometric functions 4F3(1) and 3F2(1) by applying the generalizations of Kummer's second summation theorem for 2F1(1/2) to a known transformational formula of the generalized hypergeometric function 4F3(x) recorded in the book of Rainville. Further, we apply these results to evaluate some specific forms of 4F3(1) and 3F2(1). Our results are derived with the help of binomial theorem and certain properties of gamma function.