Computes recursively and stores normalization constants for fully-normalized spherical harmonics. More...

#include <Nlm.hpp>

Public Member Functions
	Nlm ()

	Nlm (int l_max)

Nlm &	operator= (const Nlm &other)

	Nlm (const Nlm &other)

double	get_Nlm (int l, int m)
	Getter for normalization constant.

Detailed Description

Computes recursively and stores normalization constants for fully-normalized spherical harmonics.

This class computes the normalization constants for fully-normalized spherical harmonics as defined in Heiskanen and Moritz (1967, eq. 1-91). As a result, the orthogonality integrals values are:

\[ \frac{1}{4\pi} \iint \bar{Y}_{lm}(\phi,\theta) \bar{Y}_{l'm'}(\phi,\theta) \, d\sigma = \delta_{ll'}\delta_{mm'} \]

The normalization constants take the following form:

\[ N_{lm} = \sqrt{\frac{(2-\delta_{0m})(2l+1)(l+m)!}{(l-m)!}} \]

This class leverages recursive relations to compute all the normalization constants up to a maximum input degree minimizing the overflow problem.

Constructor & Destructor Documentation

◆ Nlm() [1/2]

Nlm::Nlm ( )

Default constructor

◆ Nlm() [2/2]

Nlm::Nlm ( int l_max )

Class constructor

Parameters

l_max Maximum degree and order to which the normalization constants are computed

Member Function Documentation

◆ get_Nlm()

double Nlm::get_Nlm	(	int	l,
		int	m
	)

Getter for normalization constant.