Communications of the
Korean Mathematical Society CKMS

Generating functions play an important role in the investigation of various useful properties of the sequences which they generate. Exton \cite{Exto-93} presented a very general double generating relation involving products of two Laguerre polynomials. Motivated essentially by Exton's derivation \cite{Exto-93}, the authors aim to show how one can obtain nineteen new generating relations associated with products of two Laguerre polynomials in the form of a single result. We also consider some interesting and potentially useful special cases of our main findings.

Keywords: gamma function, hypergeometric function, generalized hypergeometric function, Kamp\'e de F\'eriet function, Kummer's second summation theorem, Dixon and Whipple's summation theorems

MSC numbers: Primary 33B20, 33C20; Secondary 33B15, 33C05