assoc_legendrepoly.cc

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#include "legendrepoly.h"
#include <cmath>
#include <cstdlib>
 
//###################################################################
/**Provides the function evaluation of the associated Legendre polynomial at value x.
 
 
This code has a whitepaper associated with it
<a href="SphericalHarmonics.pdf" target="_blank"><b>Spherical Harmonics</b></a>
 
 
 \param ell int The ell order of the polynomial.
 \param m int The m-th moment of the polynomial
 \param x double The evaluation point.*/
double chi_math::AssocLegendre(unsigned int ell, int m, double x)
{
  if (abs(m)>ell) return 0.0;
 
  //===== ell=0, m=0
  if (ell==0) return 1.0;
 
 
 
  //===== ell=1, m=0,
  double Pn = x;
 
  //===== ell=1, m=1
  double Pnpos = -sqrt(1.0 - x*x);
 
  if (ell==1)
  {
    if (m== 0) return Pn;
    if (m== 1) return Pnpos;
  }
 
  double Pmlp1;
  if (ell==m)
  {
    Pmlp1 = -(2.0*ell-1.0)*sqrt(1.0 - x*x) *
      AssocLegendre(ell-1,int(ell)-1,x);
  }
  else
  {
    Pmlp1 = (2.0*ell-1.0)*x*AssocLegendre(ell-1,m,x);
    Pmlp1 = Pmlp1 - (ell+m-1)*AssocLegendre(ell-2,m,x);
    Pmlp1 = Pmlp1 / (ell-m);
  }
 
  return Pmlp1;
}