Some applications of Legendre numbers

Paul W. Haggard

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-8

Abstract:

The associated Legendre functions are defined using the Legendre numbers. From these the associated Legendre polynomials are obtained and the derivatives of these polynomials at x = 0 are derived by using properties of the Legendre numbers. These derivatives are then used to expand the associated Legendre polynomials and x n in series of Legendre polynomials. Other applications include evaluating certain integrals, expressing polynomials as linear combinations of Legendre polynomials, and expressing linear combinations of Legendre polynomials as polynomials. A connection between Legendre and Pascal numbers is also given.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:538097

DOI: 10.1155/S0161171288000481

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