# A new Fortran 90 program to compute regular and irregular associated Legendre functions

## Description

Abstract We present a modern Fortran 90 code to compute the regular Plm(x) and irregular Qlm(x) associated Legendre functions for all x∈(-1,+1) (on the cut) and |x|>1 and integer degree (l) and order (m). The code applies either forward or backward recursion in (l) and (m) in the stable direction, starting with analytically known values for forward recursion and considering both a Wronskian based and a modified Miller's method for backward recursion. While some Fortran 77 codes existed for computing t... Title of program: Associated Legendre Functions Catalogue Id: AEHE_v1_0 Nature of problem Compute the regular and irregular associated Legendre functions for integer values of the degree and order and for all real arguments. The computation of the interaction of two electrons, 1/|r1 - r2|, in prolate spheroidal coordinates is used as one example where these functions are required for all values of the argument and we are able to easily compare the series expansion in associated Legendre functions and the exact value. Versions of this program held in the CPC repository in Mendeley Data AEHE_v1_0; Associated Legendre Functions; 10.1016/j.cpc.2010.08.038 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)