Generalized Summation Formulas for the Kampé de Fériet Function

Abstract

By employing two well-known Euler’s transformations for the hypergeometric function 2F1, Liu and Wang established numerous general transformation and reduction formulas for the Kampé de Fériet function and deduced many new summation formulas for the Kampé de Fériet function with the aid of classical summation theorems for the 2F1 due to Kummer, Gauss and Bailey. Here, by making a fundamental use of the above-mentioned reduction formulas, we aim to establish 32 general summation formulas for the Kampé de Fériet function with the help of generalizations of the above-referred summation formulas for the 2F1 due to Kummer, Gauss and Bailey. Relevant connections of some particular cases of our main identities, among numerous ones, with those known formulas are explicitly indicated.

Keywords

• Gamma function
• Pochhammer symbol
• Gauss’s hypergeometric function ₂<i>F</i>₁
• generalized hypergeometric function <i>_pF_q</i>
• Kampé de Fériet function
• generalization of Kummer’s summation theorem