The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Table of Contents - 1991 - Volume 32, Issue 03  

Research Article

Some integrals involving Legendre polynomials providing combinatorial identities

Anthony D. Klemma1 and Sigurd Y. Larsena2

a1 Division of Computing and Mathematics, Deakin University, Geelong, Victoria, 3217, Australia.

a2 Department of Physics, Temple University, Philadelphia, PA, 19122, USA.

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.

(Received August 08 1989)

(Revised March 04 1990)