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文章基本信息

  • 标题:Some applications of Legendre numbers
  • 本地全文:下载
  • 作者:Paul W. Haggard
  • 期刊名称:International Journal of Mathematics and Mathematical Sciences
  • 印刷版ISSN:0161-1712
  • 电子版ISSN:1687-0425
  • 出版年度:1988
  • 卷号:11
  • 期号:2
  • 页码:405-412
  • DOI:10.1155/S0161171288000481
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    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.

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