spherical_harmonics.cc

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#include "legendrepoly.h"
 
#include "math/chi_math.h"
#include <cmath>
 
//###################################################################
/**Implementation of the tesseral spherical harmonics.
 *
 * This code has a whitepaper associated with it
 * <a href="SphericalHarmonics.pdf" target="_blank"><b>Spherical Harmonics</b></a>
 * */
double chi_math::Ylm(unsigned int ell, int m, double varphi, double theta)
{
  const int _ell = static_cast<int>(ell);
  const int _m   = std::abs(m);
  const double Plm = AssocLegendre(ell,_m,cos(theta));
 
  if (m<0)
  {
    return pow(-1.0, _m) *
           sqrt(2.0 * Factorial(_ell - _m)/
                      Factorial(_ell + _m) ) *
           Plm * sin(_m * varphi);
  }
  else if (m==0)
  {
    return Plm;
  }
  else
  {
    return pow(-1.0, _m) *
           sqrt(2.0 * Factorial(_ell - _m)/
                      Factorial(_ell + _m) ) *
           Plm * cos(_m * varphi);
  }
}