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 $n_{x} = \sin θ \cos ϕ$ , $n_{y} = \sin θ \sin ϕ$ , and $n_{z} = \cos θ$ . 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