连带Legendre函数的高精度计算

计算物理 ›› 1999, Vol. 16 ›› Issue (1): 59-65.

连带Legendre函数的高精度计算

朱世德, 向安平, 杨进

成都气象学院基础科学系, 610041

收稿日期:1997-03-19 修回日期:1998-07-31 出版日期:1999-01-25 发布日期:1999-01-25
作者简介:朱世德,男,52,副教授

High accurate algorithm of associated legendre functions

Zhu shide, Xiang Anping, Yang Jin

Department of Basic Sciences, Chengdu Institute of Meteorology, 610041

Received:1997-03-19 Revised:1998-07-31 Online:1999-01-25 Published:1999-01-25

摘要/Abstract

摘要： 给出了计算复数次整数阶连带Legendre函数P_ν^m(cosθ)和Q_ν^m(cosθ)的高精度算法。计算结果表明,在486以上的微机上,如采用双精度,至少可精确到小数点后9位有效数字。

关键词: 连带Legendre函数, 超几何级数, Gaus公式, Gaus连续分数法

Abstract: A high accurate algorithm of calculating the associated Legendre functions for integral order and complex degree is presented. On a microcomputer and using double precision, the calculated results indicate the precision of at least 9 significant digits is attained.

Key words: associated Legendre function, hypergeometric series, Gauss formula, Gauss continued fraction method

中图分类号:

O174.6

朱世德, 向安平, 杨进. 连带Legendre函数的高精度计算[J]. 计算物理, 1999, 16(1): 59-65.

Zhu shide, Xiang Anping, Yang Jin. High accurate algorithm of associated legendre functions[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1999, 16(1): 59-65.