旋转椭球函数的数值计算

Numerical Computation of Spheroidal Wave Functions

本文给出了计算旋转长椭球和扁椭球函数的程序流图和相应的有用数学公式,并讨论了算法.所编FORTRAN程序具有适应参变量范围较宽和可获较高精度的数值结果.

The prolate and oblate spheroidal functions are of importance in the analysis of electromagnetic or acoustical wave scattering from a spheroidal body and some boundary value problems involving a spheroidal body. In this paper,the program flowchart and some useful expressions for computing these two functions are presented,and the algorithms are discussed. The tabulations given earlier by C. Flammer have been extended, and the numerical values of the oblate as well as prolate radial and angular functions have been given to 8-digit accuracy.