# Evaluation of legendre functions of argument greater than one

## Description

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)