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Some applications of Legendre numbers

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  • Paul W. Haggard

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.

Suggested Citation

  • Paul W. Haggard, 1988. "Some applications of Legendre numbers," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:538097
    DOI: 10.1155/S0161171288000481
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