A note on a series containing the Laguerre polynomials

Abstract

Expressions for the summation of a new series involving the Laguerre polynomials are obtained in terms of generalized hypergeometric functions. These results provide alternative, and in some cases simpler, expressions to those recently obtained in the literature. Mathematics Subject Classification: 33C15, 33C20

An extension of a series containing Laguerre polynomials

“…Recently, Brychkov [1] has extended these results for any integer p ≥ 0. Alternative expressions for S(±ν, ±p), also for arbitrary integer p ≥ 0, in terms of generalized hypergeometric functions of argument −x 2 have been obtained in [4]. These results differ from, and in some cases are simpler than, those obtained in [1].…”