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
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 xn 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.
