A computer program to calculate zeroes, extrema, and interval integrals for the associated Legendre functions

Abstract

A computer program is described for the calculation of the zeroes of the associated Legendre functions, Pnm, and their derivatives, for the calculation of the extrema of Pnm and also the integral between pairs of successive zeroes. The program has been run for all n,m from (0,0) to (20,20) and selected cases beyond that for n up to 40. Up to (20,20), the program (written in double precision) retains nearly full accuracy, and indications are that up to (40,40) there is still sufficient precision (4-5 decimal digits for a 54-bit mantissa) for estimation of various bounds and errors involved in geopotential modelling, the purpose for which the program was written.