Product of polynomials regular on the surface of a sphere. More...

#include <YlmTestFunctions.hpp>

Public Member Functions
	ProductOfPolynomials (size_t pow_nx, size_t pow_ny, size_t pow_nz)

DataVector	operator() (const DataVector &theta, const DataVector &phi) const

template<typename Fr >
DataVector	operator() (const tnsr::I< DataVector, 2, Fr > &theta_and_phi) const

DataVector	df_dth (const DataVector &theta, const DataVector &phi) const

template<typename Fr >
DataVector	df_dth (const tnsr::I< DataVector, 2, Fr > &theta_and_phi) const

DataVector	df_dph (const DataVector &theta, const DataVector &phi) const

template<typename Fr >
DataVector	df_dph (const tnsr::I< DataVector, 2, Fr > &theta_and_phi) const

double	definite_integral () const

Detailed Description

Product of polynomials regular on the surface of a sphere.

Details

Computes \( n_x^{k_x} n_y^{k_y} n_z^{k_z} \) where \(n_x = \sin \theta \cos \phi\), \(n_y = \sin \theta \sin \phi\), and \(n_z = \cos \theta\). The function and its first derivatives are exactly representable by spherical harmonics of order \((L,M)\) if \(L > k_x + k_y + k_z\) and \(M > k_x + k_y\).

The documentation for this class was generated from the following file:

tests/Unit/Helpers/NumericalAlgorithms/SphericalHarmonics/YlmTestFunctions.hpp

Public Member Functions

Detailed Description

Details