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Some integrals involving Legendre polynomials providing combinatorial identities

Published online by Cambridge University Press:  17 February 2009

Anthony D. Klemm  and
Sigurd Y. Larsen
Anthony D. Klemm
Affiliation:
Division of Computing and Mathematics, Deakin University, Geelong, Victoria, 3217, Australia.
Sigurd Y. Larsen
Affiliation:
Department of Physics, Temple University, Philadelphia, PA, 19122, USA.
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 3 , January 1991 , pp. 304 - 310
Copyright
Copyright © Australian Mathematical Society 1991

References

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[3]Olver, F. W. J., J. of Res. NBS-B 17B (1967) 111.Google Scholar