Reducibility of Certain Kampe De Feriet Function with an Application to Generating relations for products of two Laguerre polynomials

Abstract

It has been an interesting and natural research subject to consider the reducibility of some extensively generalized special functions. In this regard, Kamp\'e de F\'eriet function has been attracted by many mathematicians. The authors \cite{Ch-Ra-14} also established many interesting cases of the reducibility of Kamp\'e de F\'eriet function by employing generalizations of the two results for the terminating ${}_2F_1(2)$ hypergeometric identities due to Kim et al. In this sequel, we first aim at presenting several interesting cases of the reducibility of Kamp\'e de F\'eriet function by using generalizations of classical Kummer's summation theorem due to Lavoie et al.

We next show how one can use the above-given result to obtain eleven new generating relations for products of two Laguerre polynomials in a single-form result. We also consider many interesting and potentially useful specials cases of our main results.