Routines Using Associated Legendre Functions and Legendre Polynomials.

摘要

Computer routines are described which involve Associated Legendre functions of the first kind. Included are a routine to expand functions in Legendre polynomials, routines for the real and imaginary parts of the spherical harmonics in spherical polar coordinates, derivatives of the Legendre polynomials and multiple integrals of Legendre polynomials P/sub k/(X) multiplied by a positive integer power of X. The derivations of the mathematical formulae used are included. (ERA citation 03:020826)