J Austral Math Soc Ser B 32 pp304--310, 1991.

Some integrals involving Legendre polynomials providing combinatorial identities

Anthony D. Klemm and Sigurd Y. Larsen

Abstract

An integral involving a combination of Legendre polynomials, exponential and algebraic terms is solved using the generating function. Special cases of this result are compared with known expansions, and the previously known results are shown to be extendible to a particularly pleasing result as a limiting case. Comparisons provide some new combinatorial identities involving binomials. Finally, an effective numerical procedure is described which evaluates the integral to machine accuracy.

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Authors

Anthony D. Klemm

Division of Computing and Mathematics, Deakin University, Geelong, Victoria, 3217, Australia.

Sigurd Y. Larsen

Department of Physics, Temple University, Philadelphia, PA, 19122, USA.