Evaluation of legendre functions of argument greater than one

Abstract
In this paper we present an algorithm to evaluate Legendre functions of the first and second kinds (P_v ,Q_v ) for integral and half-integral order and argument greater than one. The code is based on the calculation of the continued fraction for the Q's, the Wronskian relating P's and Q's and the application of forward recurrence relations for the P's and backward recurrence for the Q's. We also show an application of these algorithms to the evaluation of the electrostatic field due to a char...

Title of program: DLEGENI, DLEGENS
Catalogue Id: ADGO_v1_0

Nature of problem
We include two codes in order to evaluate: 1) Legendre functions of half-integral order (subroutine DLEGENS) 2) Legendre functions of integral order (subroutine DLEGENI) Both codes evaluate Legendre functions of the first and second kinds from the lower (positive) orders to a maximum order NMAX in the same run. The algorithms find their application in problems with a spheroidal (integral order) or toroidal (semi-integral order) geometry. We show as an example the application of subroutine DLEGEN ...

Versions of this program held in the CPC repository in Mendeley Data
ADGO_v1_0; DLEGENI, DLEGENS; 10.1016/S0010-4655(97)00076-3

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

**摘要**
本文提出一种针对宗量大于1的整数阶与半整数阶第一类、第二类勒让德函数（Legendre functions，$P_v, Q_v$）的数值计算算法。该算法基于三项核心内容：第二类勒让德函数$Q_v$的连分数（continued fraction）计算、关联第一类与第二类勒让德函数的朗斯基行列式（Wronskian），以及对第一类勒让德函数采用前向递推关系、对第二类勒让德函数采用后向递推关系。本文还展示了该算法在由带电[原文截断为"char"]源产生的静电场求值中的应用……

**程序名称**：DLEGENI、DLEGENS
**目录编号**：ADGO_v1_0

**程序解决的问题**
本程序包含两个子程序以实现两类功能：1）半整数阶勒让德函数（对应子程序DLEGENS）；2）整数阶勒让德函数（对应子程序DLEGENI）。两个子程序均可在单次运行中，从正低阶至最大阶数NMAX完成第一类与第二类勒让德函数的求值。本算法可应用于椭球几何（整数阶场景）或环面几何（半整数阶场景）相关问题。本文以子程序DLEGEN的应用为例……（原文截断）

**Mendeley数据中CPC程序库内的本程序版本**：ADGO_v1_0；DLEGENI、DLEGENS；10.1016/S0010-4655(97)00076-3

**本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2019）**