Special Cases on the Product of Two Confluent Hypergeometric Functions

Abstract

The hypergeometric function, represented as 2 F1(a,b;c;z), is a specialized function that emerges in various fields including probability, combinatorics, engineering and mathematical physics. It serves as a generalization of the geometric series and fulfills a second-order linear differential equation. The product of hypergeometric functions frequently arises, particularly in relation to summation identities, integral transforms, or representation theory. These products can uncover profound symmetries and connections among special functions, playing a crucial role in addressing intricate challenges in both pure and applied mathematics. This study, building on the contributions of Poudel et al., seeks to elucidate specific cases of various product formulas assigning the different values of the parameters that involved in two confluent hypergeometric functions.
Keywords: , , , .