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
本论文提出一种算法，用于评估第一类和第二类勒让德函数（(P_v, Q_v)）的积分和半积分阶，以及大于一的参数。该算法基于对 (Q) 的连分式计算、关联 (P) 和 (Q) 的朗斯基行列式以及 (P) 的前向递推关系和 (Q) 的后向递推关系的应用。此外，我们还展示了这些算法在评估由电荷产生的静电场中的应用。
程序名称：DLEGENI, DLEGENS
目录编号：ADGO_v1_0
问题性质
为了评估，我们包括两个代码：1) 半积分阶勒让德函数（子程序 DLEGENS）2) 积分阶勒让德函数（子程序 DLEGENI）。两个代码均在同一运行中评估从低阶（正阶）到最大阶数 (NMAX) 的第一类和第二类勒让德函数。这些算法在具有球状（积分阶）或环状（半积分阶）几何的问题中找到其应用。以下是一个示例，展示了子程序 DLEGEN ... 的应用。
Mendeley 数据中 CPC 存储库中保存的此程序的版本
ADGO_v1_0; DLEGENI, DLEGENS; 10.1016/S0010-4655(97)00076-3
此程序已从贝尔法斯特女王大学（1969-2019）的 CPC 程序库中导入。