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

摘要

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 the functions off the cut, no Fortran 90 code was available for accurately computing the functions for all real values of x different from x=±1 where the irregular functions are not defined.