function f=plgndr(l,m,x)
% return the Ferrer definition of the associated Legendre function.
% function f=plgndr(l,m,x)
% (c) 2008 Alain Hebert, Ecole Polytechnique de Montreal
  if m < 0
    error('bad arguments in plgndr 1')
  elseif m > l
    error('bad arguments in plgndr 2')
  elseif abs(x) > 1.
    error('bad arguments in plgndr 3')
  end
  pmm=1. ;
  if m > 0, pmm=prod(1:2:2*m)*sqrt((1.-x).*(1.+x)).^m ; end
  if l == m
    f=pmm ;
  else
    pmmp1=(2*m+1)*x.*pmm ;
    if l == m+1
      f=pmmp1 ;
    else
      for ll=m+2:l
        pll=((2*ll-1)*x.*pmmp1-(ll+m-1)*pmm)/(ll-m) ;
        pmm=pmmp1 ; pmmp1=pll ;
      end
      f=pll ;
    end
  end