# Evaluation of toroidal harmonics

## Description

Abstract Three algorithms to evaluate toroidal harmonics, i.e., Legendre functions of integral order and half-odd degree of the first and second kinds for real arguments larger than one, are presented. The first algorithm (DTORH1) allows the evaluation of the set {P_(n-1/2) ^m (x), Q_(n-1/2) ^m (x)} for fixed (integer and positive) values of m and n = 0, 1, ..., N. The algorithms DTORH2 and DTORH3 extend the method used in DTORH1 to obtain th... Title of program: DTORH1, DTORH2, DTORH3 Catalogue Id: ADKV_v1_0 Nature of problem We include three codes to evaluate toroidal harmonics: <ul type="circle"><li>DTORH1: This code evaluates toroidal harmonics (TH) of the first and second kinds for a given order m, from the lowest (positive) degreee (n=0) to a maximum degree n = N in the same run. <li>DTORH2: This code evaluates toroidal harmonics of the first and second kinds Pm(n-1/2)(x) and Qm(n-1/2)(x) for orders m = 0,...,M and degrees n = 0,...,N. In this code, for each given order m, TH up to the maximum degree reached by ... Versions of this program held in the CPC repository in Mendeley Data ADKV_v2_0; DTORH3 v 2.0; 10.1016/S0010-4655(01)00188-6 ADKV_v1_0; DTORH1, DTORH2, DTORH3; 10.1016/S0010-4655(99)00428-2 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)