On a new class of summation formulae involving the Laguerre polynomial

Abstract

By elementary manipulation of series, a general transformation involving the generalized hypergeometric function is established. Kummer's first theorem, the classical Gauss summation theorem and the generalized Kummer summation theorem due to Lavoie, Grondin and Rathie [J. Comput. Appl. Math. 72 (1996) 293-300] are then applied to obtain a new class of summation formulae involving the Laguerre polynomial, which have not previously appreared in the literature. Several related results due to Exton have also been given in corrected form.

A note on a series containing the Laguerre polynomials

“…for any non-negative integer j. Our results are different from, and in some cases simpler than, those obtained in [1] and [3].…”

“…In [3], Kim et al obtained summation formulas for the series involving the generalized Laguerre polynomial…”

An extension of a series containing Laguerre polynomials

“…In [3], Kim et al obtained summation formulas for the series involving the generalized Laguerre polynomial L (ν) n (x) given by ∞ n=0…”