COMPUTING THE CONICAL FUNCTION P-1/2+iτμ (x)

被引：10

作者：

Gil, Amparo ^{[1
]}

Segura, Javier ^{[2
]}

Temme, Nico M. ^{[3
]}

机构：

[1] Univ Cantabria, ETSI Caminos, Dept Matemat Aplicada & CC Computac, E-39005 Santander, Spain

[2] Univ Cantabria, Dept Matemat Estadist & Computac, E-39005 Santander, Spain

[3] CWI, NL-1090 GB Amsterdam, Netherlands

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2009年 / 31卷 / 03期

关键词：

Legendre functions; conical functions; hypergeometric functions; modified Bessel functions; three-term recurrence relations; difference equations; stability of recurrence relations; numerical evaluation of special functions; asymptotic analysis; MODIFIED BESSEL-FUNCTIONS;

D O I：

10.1137/070712006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A stable computational scheme for the conical function P--1/2+i tau(mu) (x) for x > -1, real tau, and mu <= 0 or mu is an element of N is presented. The scheme combines uniform asymptotic expansions for large vertical bar mu vertical bar with the application of the three-term recurrence relation on the mu index in the direction of decreasing vertical bar mu vertical bar when x > 0. When x < 0, the conditioning of recursion is the opposite, and conical functions can be computed in the direction of increasing vertical bar mu vertical bar.

引用

页码：1716 / 1741

页数：26

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