Some applications of Legendre numbers

[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 atx=0are derived by using properties of the Legendre numbers. These derivatives are then used to expand the associated Legendre polynomials andxnin 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.

[学科分类] 数学（综合）