Legendre functions. More...

Typedefs
typedef gsl_sf_legendre_t	legendre_t
	Alias. More...

Functions
legendre_t const	SCHMIDT ()
	Type. More...

legendre_t const	SPHARM ()
	Type. More...

legendre_t const	FULL ()
	Type. More...

legendre_t const	NONE ()
	Type. More...

int	Pl_e (int const l, double const x, result &result)
	C++ version of gsl_sf_legendre_Pl_e(). More...

double	Pl (int const l, double const x)
	C++ version of gsl_sf_legendre_Pl(). More...

template<typename DATA >
int	Pl_array (int const lmax, double const x, DATA &result_array)
	C++ version of gsl_sf_legendre_Pl_array(). More...

template<typename DATA >
int	Pl_deriv_array (int const lmax, double const x, DATA &result_array, DATA &result_deriv_array)
	C++ version of gsl_sf_legendre_Pl_deriv_array(). More...

int	P1_e (double x, result &result)
	C++ version of gsl_sf_legendre_P1_e(). More...

int	P2_e (double x, result &result)
	C++ version of gsl_sf_legendre_P2_e(). More...

int	P3_e (double x, result &result)
	C++ version of gsl_sf_legendre_P3_e(). More...

double	P1 (double const x)
	C++ version of gsl_sf_legendre_P1(). More...

double	P2 (double const x)
	C++ version of gsl_sf_legendre_P2(). More...

double	P3 (double const x)
	C++ version of gsl_sf_legendre_P3(). More...

int	Q0_e (double const x, result &result)
	C++ version of gsl_sf_legendre_Q0_e(). More...

double	Q0 (double const x)
	C++ version of gsl_sf_legendre_Q0(). More...

int	Q1_e (double const x, result &result)
	C++ version of gsl_sf_legendre_Q1_e(). More...

double	Q1 (double const x)
	C++ version of gsl_sf_legendre_Q1(). More...

int	Ql_e (int const l, double const x, result &result)
	C++ version of gsl_sf_legendre_Ql_e(). More...

double	Ql (int const l, double const x)
	C++ version of gsl_sf_legendre_Ql(). More...

int	Plm_e (int const l, int const m, double const x, result &result)
	C++ version of gsl_sf_legendre_Plm_e(). More...

double	Plm (int const l, int const m, double const x)
	C++ version of gsl_sf_legendre_Plm(). More...

template<typename DATA >
int	Plm_array (int const lmax, int const m, double const x, DATA &result_array)
	C++ version of gsl_sf_legendre_Plm_array(). More...

template<typename DATA >
int	Plm_deriv_array (int const lmax, int const m, double const x, DATA &result_array, DATA &result_deriv_array)
	C++ version of gsl_sf_legendre_Plm_deriv_array(). More...

int	sphPlm_e (int const l, int m, double const x, result &result)
	C++ version of gsl_sf_legendre_sphPlm_e(). More...

double	sphPlm (int const l, int const m, double const x)
	C++ version of gsl_sf_legendre_sphPlm(). More...

int	array_size (int const lmax, int const m)
	C++ version of gsl_sf_legendre_array_size(). More...

int	H3d_0_e (double const lambda, double const eta, result &result)
	C++ version of gsl_sf_legendre_H3d_0_e(). More...

double	H3d_0 (double const lambda, double const eta)
	C++ version of gsl_sf_legendre_H3d_0(). More...

int	H3d_1_e (double const lambda, double const eta, result &result)
	C++ version of gsl_sf_legendre_H3d_1_e(). More...

double	H3d_1 (double const lambda, double const eta)
	C++ version of gsl_sf_legendre_H3d_1(). More...

int	H3d_e (int const l, double const lambda, double const eta, result &result)
	C++ version of gsl_sf_legendre_H3d_e(). More...

double	H3d (int const l, double const lambda, double const eta)
	C++ version of gsl_sf_legendre_H3d(). More...

template<typename DATA >
int	H3d_array (int const lmax, double const lambda, double const eta, DATA &result_array)
	C++ version of gsl_sf_legendre_H3d_array(). More...

template<typename DATA >
int	array (legendre_t const norm, size_t const lmax, double const x, DATA &result_array)
	C++ version of gsl_sf_legendre_array(). More...

template<typename DATA >
int	array_e (legendre_t const norm, size_t const lmax, double const x, double const csphase, DATA &result_array)
	C++ version of gsl_sf_legendre_array_e(). More...

template<typename DATA >
int	deriv_array (legendre_t const norm, size_t const lmax, double const x, DATA &result_array, DATA &result_deriv_array)
	C++ version of gsl_sf_legendre_deriv_array(). More...

template<typename DATA >
int	deriv_array_e (legendre_t const norm, size_t const lmax, double const x, double const csphase, DATA &result_array, DATA &result_deriv_array)
	C++ version of gsl_sf_legendre_deriv_array_e(). More...

template<typename DATA >
int	deriv_alt_array (legendre_t const norm, size_t const lmax, double const x, DATA &result_array, DATA &result_deriv_array)
	C++ version of gsl_sf_legendre_deriv_alt_array(). More...

template<typename DATA >
int	deriv_alt_array_e (legendre_t const norm, size_t const lmax, double const x, double const csphase, DATA &result_array, DATA &result_deriv_array)
	C++ version of gsl_sf_legendre_deriv_alt_array_e(). More...

template<typename DATA >
int	deriv2_array (legendre_t const norm, size_t const lmax, double const x, DATA &result_array, DATA &result_deriv_array, DATA &result_deriv2_array)
	C++ version of gsl_sf_legendre_deriv2_array(). More...

template<typename DATA >
int	deriv2_array_e (legendre_t const norm, size_t const lmax, double const x, double const csphase, DATA &result_array, DATA &result_deriv_array, DATA &result_deriv2_array)
	C++ version of gsl_sf_legendre_deriv2_array_e(). More...

template<typename DATA >
int	deriv2_alt_array (legendre_t const norm, size_t const lmax, double const x, DATA &result_array, DATA &result_deriv_array, DATA &result_deriv2_array)
	C++ version of gsl_sf_legendre_deriv2_alt_array(). More...

template<typename DATA >
int	deriv2_alt_array_e (legendre_t const norm, size_t const lmax, double const x, double const csphase, DATA &result_array, DATA &result_deriv_array, DATA &result_deriv2_array)
	C++ version of gsl_sf_legendre_deriv2_alt_array_e(). More...

size_t	array_n (size_t const lmax)
	C++ version of gsl_sf_legendre_array_n(). More...

size_t	array_index (size_t const l, size_t const m)
	C++ version of gsl_sf_legendre_array_index(). More...

size_t	nlm (size_t const lmax)
	C++ version of gsl_sf_legendre_nlm(). More...

Detailed Description

Legendre functions.

Typedef Documentation

◆ legendre_t

typedef gsl_sf_legendre_t gsl::sf::legendre::legendre_t

Alias.

Definition at line 36 of file sf_legendre.hpp.

Function Documentation

◆ array()

template<typename DATA >

int gsl::sf::legendre::array	(	legendre_t const	norm,
		size_t const	lmax,
		double const	x,
		DATA &	result_array
	)

inline

C++ version of gsl_sf_legendre_array().

Parameters

norm	Normalisation type
lmax	Maximum value of l parameter
x	Value in (–1,1)
result_array	Array for result

Returns: GSL_SUCCESS or error code

Definition at line 731 of file sf_legendre.hpp.

◆ array_e()

template<typename DATA >

int gsl::sf::legendre::array_e	(	legendre_t const	norm,
		size_t const	lmax,
		double const	x,
		double const	csphase,
		DATA &	result_array
	)

inline

C++ version of gsl_sf_legendre_array_e().

Parameters

norm	Normalisation type
lmax	Maximum value of l parameter
x	Value in (–1,1)
csphase	Parameter for Condon–Shortley phase factor
result_array	Array for result

Returns: GSL_SUCCESS or error code

Definition at line 760 of file sf_legendre.hpp.

◆ array_index()

size_t gsl::sf::legendre::array_index	(	size_t const	l,
		size_t const	m
	)

inline

C++ version of gsl_sf_legendre_array_index().

Parameters

l	Index l
m	Index m

Returns: Index in array

Definition at line 1058 of file sf_legendre.hpp.

◆ array_n()

size_t gsl::sf::legendre::array_n ( size_t const lmax )

inline

C++ version of gsl_sf_legendre_array_n().

Parameters

lmax	Maximum value of l parameter

Returns: Minimum result array size

Definition at line 1051 of file sf_legendre.hpp.

◆ array_size()

int gsl::sf::legendre::array_size	(	int const	lmax,
		int const	m
	)

inline

C++ version of gsl_sf_legendre_array_size().

size of result_array needed for the array versions of Plm (lmax - m + 1)

Parameters

lmax	An integer
m	An integer

Returns: GSL_SUCCESS

Definition at line 415 of file sf_legendre.hpp.

◆ deriv2_alt_array()

template<typename DATA >

int gsl::sf::legendre::deriv2_alt_array	(	legendre_t const	norm,
		size_t const	lmax,
		double const	x,
		DATA &	result_array,
		DATA &	result_deriv_array,
		DATA &	result_deriv2_array
	)

inline

C++ version of gsl_sf_legendre_deriv2_alt_array().

Parameters

norm	Normalisation type
lmax	Maximum value of l parameter
x	Value in (–1,1)
result_array	Array for result
result_deriv_array	Array for result
result_deriv2_array	Array for result

Returns: GSL_SUCCESS or error code

Definition at line 1000 of file sf_legendre.hpp.

◆ deriv2_alt_array_e()

template<typename DATA >

int gsl::sf::legendre::deriv2_alt_array_e	(	legendre_t const	norm,
		size_t const	lmax,
		double const	x,
		double const	csphase,
		DATA &	result_array,
		DATA &	result_deriv_array,
		DATA &	result_deriv2_array
	)

inline

C++ version of gsl_sf_legendre_deriv2_alt_array_e().

Parameters

norm	Normalisation type
lmax	Maximum value of l parameter
x	Value in (–1,1)
csphase	Parameter for Condon–Shortley phase factor
result_array	Array for result
result_deriv_array	Array for result
result_deriv2_array	Array for result

Returns: GSL_SUCCESS or error code

Definition at line 1037 of file sf_legendre.hpp.

◆ deriv2_array()

template<typename DATA >

int gsl::sf::legendre::deriv2_array	(	legendre_t const	norm,
		size_t const	lmax,
		double const	x,
		DATA &	result_array,
		DATA &	result_deriv_array,
		DATA &	result_deriv2_array
	)

inline

C++ version of gsl_sf_legendre_deriv2_array().

Parameters

norm	Normalisation type
lmax	Maximum value of l parameter
x	Value in (–1,1)
result_array	Array for result
result_deriv_array	Array for result
result_deriv2_array	Array for result

Returns: GSL_SUCCESS or error code

Definition at line 924 of file sf_legendre.hpp.

◆ deriv2_array_e()

template<typename DATA >

int gsl::sf::legendre::deriv2_array_e	(	legendre_t const	norm,
		size_t const	lmax,
		double const	x,
		double const	csphase,
		DATA &	result_array,
		DATA &	result_deriv_array,
		DATA &	result_deriv2_array
	)

inline

C++ version of gsl_sf_legendre_deriv2_array_e().

Parameters

norm	Normalisation type
lmax	Maximum value of l parameter
x	Value in (–1,1)
csphase	Parameter for Condon–Shortley phase factor
result_array	Array for result
result_deriv_array	Array for result
result_deriv2_array	Array for result

Returns: GSL_SUCCESS or error code

Definition at line 963 of file sf_legendre.hpp.

◆ deriv_alt_array()

template<typename DATA >

int gsl::sf::legendre::deriv_alt_array	(	legendre_t const	norm,
		size_t const	lmax,
		double const	x,
		DATA &	result_array,
		DATA &	result_deriv_array
	)

inline

C++ version of gsl_sf_legendre_deriv_alt_array().

Parameters

norm	Normalisation type
lmax	Maximum value of l parameter
x	Value in (–1,1)
result_array	Array for result
result_deriv_array	Array for result

Returns: GSL_SUCCESS or error code

Definition at line 855 of file sf_legendre.hpp.

◆ deriv_alt_array_e()

template<typename DATA >

int gsl::sf::legendre::deriv_alt_array_e	(	legendre_t const	norm,
		size_t const	lmax,
		double const	x,
		double const	csphase,
		DATA &	result_array,
		DATA &	result_deriv_array
	)

inline

C++ version of gsl_sf_legendre_deriv_alt_array_e().

Parameters

norm	Normalisation type
lmax	Maximum value of l parameter
x	Value in (–1,1)
csphase	Parameter for Condon–Shortley phase factor
result_array	Array for result
result_deriv_array	Array for result

Returns: GSL_SUCCESS or error code

Definition at line 889 of file sf_legendre.hpp.

◆ deriv_array()

template<typename DATA >

int gsl::sf::legendre::deriv_array	(	legendre_t const	norm,
		size_t const	lmax,
		double const	x,
		DATA &	result_array,
		DATA &	result_deriv_array
	)

inline

C++ version of gsl_sf_legendre_deriv_array().

Parameters

norm	Normalisation type
lmax	Maximum value of l parameter
x	Value in (–1,1)
result_array	Array for result
result_deriv_array	Array for result

Returns: GSL_SUCCESS or error code

Definition at line 789 of file sf_legendre.hpp.

◆ deriv_array_e()

template<typename DATA >

int gsl::sf::legendre::deriv_array_e	(	legendre_t const	norm,
		size_t const	lmax,
		double const	x,
		double const	csphase,
		DATA &	result_array,
		DATA &	result_deriv_array
	)

inline

C++ version of gsl_sf_legendre_deriv_array_e().

Parameters

norm	Normalisation type
lmax	Maximum value of l parameter
x	Value in (–1,1)
csphase	Parameter for Condon–Shortley phase factor
result_array	Array for result
result_deriv_array	Array for result

Returns: GSL_SUCCESS or error code

Definition at line 823 of file sf_legendre.hpp.

◆ FULL()

legendre_t const gsl::sf::legendre::FULL ( )

inline

Type.

Returns: GSL_SF_LEGENDRE_FULL

Definition at line 51 of file sf_legendre.hpp.

◆ H3d()

double gsl::sf::legendre::H3d	(	int const	l,
		double const	lambda,
		double const	eta
	)

inline

C++ version of gsl_sf_legendre_H3d().

lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

Normalization: Flat-Lim legendre_H3d_l(l,lambda,eta) = j_l(lambda*eta)

eta >= 0.0, l >= 0

Parameters

l	An integer
lambda	A real value
eta	A real value

Returns: The function value

Definition at line 678 of file sf_legendre.hpp.

References gsl::sf::eta().

◆ H3d_0()

double gsl::sf::legendre::H3d_0	(	double const	lambda,
		double const	eta
	)

inline

C++ version of gsl_sf_legendre_H3d_0().

Zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

legendre_H3d_0(lambda,eta) := sin(lambda*eta)/(lambda*sinh(eta))

Normalization: Flat-Lim legendre_H3d_0(lambda,eta) = j_0(lambda*eta)

eta >= 0.0

Parameters

lambda	A real value
eta	A real value

Returns: The function value

Definition at line 606 of file sf_legendre.hpp.

References gsl::sf::eta().

◆ H3d_0_e()

int gsl::sf::legendre::H3d_0_e	(	double const	lambda,
		double const	eta,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_H3d_0_e().

Zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

legendre_H3d_0(lambda,eta) := sin(lambda*eta)/(lambda*sinh(eta))

Normalization: Flat-Lim legendre_H3d_0(lambda,eta) = j_0(lambda*eta)

eta >= 0.0

Parameters

lambda	A real value
eta	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 589 of file sf_legendre.hpp.

References gsl::sf::eta().

◆ H3d_1()

double gsl::sf::legendre::H3d_1	(	double const	lambda,
		double const	eta
	)

inline

C++ version of gsl_sf_legendre_H3d_1().

First radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

legendre_H3d_1(lambda,eta) := 1/sqrt(lambda^2 + 1) sin(lam eta)/(lam sinh(eta)) (coth(eta) - lambda cot(lambda*eta))

Normalization: Flat-Lim legendre_H3d_1(lambda,eta) = j_1(lambda*eta)

eta >= 0.0

Parameters

lambda	A real value
eta	A real value

Returns: The function value

Definition at line 645 of file sf_legendre.hpp.

References gsl::sf::eta().

◆ H3d_1_e()

int gsl::sf::legendre::H3d_1_e	(	double const	lambda,
		double const	eta,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_H3d_1_e().

First radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

legendre_H3d_1(lambda,eta) := 1/sqrt(lambda^2 + 1) sin(lam eta)/(lam sinh(eta)) (coth(eta) - lambda cot(lambda*eta))

Normalization: Flat-Lim legendre_H3d_1(lambda,eta) = j_1(lambda*eta)

eta >= 0.0

Parameters

lambda	A real value
eta	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 626 of file sf_legendre.hpp.

References gsl::sf::eta().

◆ H3d_array()

template<typename DATA >

int gsl::sf::legendre::H3d_array	(	int const	lmax,
		double const	lambda,
		double const	eta,
		DATA &	result_array
	)

inline

C++ version of gsl_sf_legendre_H3d_array().

Array of H3d(ell), 0 <= ell <= lmax

Parameters

lmax	An integer
lambda	A real value
eta	A real value
result_array	An array of size `lmax`

Returns: GSL_SUCCESS

Definition at line 704 of file sf_legendre.hpp.

References gsl::sf::eta().

◆ H3d_e()

int gsl::sf::legendre::H3d_e	(	int const	l,
		double const	lambda,
		double const	eta,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_H3d_e().

lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

Normalization: Flat-Lim legendre_H3d_l(l,lambda,eta) = j_l(lambda*eta)

eta >= 0.0, l >= 0

Parameters

l	An integer
lambda	A real value
eta	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 662 of file sf_legendre.hpp.

References gsl::sf::eta().

◆ nlm()

size_t gsl::sf::legendre::nlm ( size_t const lmax )

inline

C++ version of gsl_sf_legendre_nlm().

Parameters

lmax	Maximum value of l parameter

Returns: UNDOCUMENTED

Definition at line 1065 of file sf_legendre.hpp.

◆ NONE()

legendre_t const gsl::sf::legendre::NONE ( )

inline

Type.

Returns: GSL_SF_LEGENDRE_NONE

Definition at line 56 of file sf_legendre.hpp.

◆ P1()

double gsl::sf::legendre::P1 ( double const x )

inline

C++ version of gsl_sf_legendre_P1().

P_l(x), l=1

Parameters

x	A real value

Returns: The function value

Definition at line 164 of file sf_legendre.hpp.

◆ P1_e()

int gsl::sf::legendre::P1_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_P1_e().

P_l(x), l=1

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 138 of file sf_legendre.hpp.

◆ P2()

double gsl::sf::legendre::P2 ( double const x )

inline

C++ version of gsl_sf_legendre_P2().

P_l(x), l=2

Parameters

x	A real value

Returns: The function value

Definition at line 171 of file sf_legendre.hpp.

◆ P2_e()

int gsl::sf::legendre::P2_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_P2_e().

P_l(x), l=2

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 147 of file sf_legendre.hpp.

◆ P3()

double gsl::sf::legendre::P3 ( double const x )

inline

C++ version of gsl_sf_legendre_P3().

P_l(x), l=3

Parameters

x	A real value

Returns: The function value

Definition at line 178 of file sf_legendre.hpp.

◆ P3_e()

int gsl::sf::legendre::P3_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_P3_e().

P_l(x), l=3

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 156 of file sf_legendre.hpp.

◆ Pl()

double gsl::sf::legendre::Pl	(	int const	l,
		double const	x
	)

inline

C++ version of gsl_sf_legendre_Pl().

P_l(x) l >= 0; |x| <= 1

Parameters

l	An integer
x	A real value

Returns: The function value

Definition at line 74 of file sf_legendre.hpp.

◆ Pl_array()

template<typename DATA >

int gsl::sf::legendre::Pl_array	(	int const	lmax,
		double const	x,
		DATA &	result_array
	)

inline

C++ version of gsl_sf_legendre_Pl_array().

P_l(x) for l=0,...,lmax; |x| <= 1

Parameters

lmax	An integer
x	A real value
result_array	An array of size `lmax`

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 97 of file sf_legendre.hpp.

◆ Pl_deriv_array()

template<typename DATA >

int gsl::sf::legendre::Pl_deriv_array	(	int const	lmax,
		double const	x,
		DATA &	result_array,
		DATA &	result_deriv_array
	)

inline

C++ version of gsl_sf_legendre_Pl_deriv_array().

P_l(x) and P_l'(x) for l=0,...,lmax; |x| <= 1

Parameters

lmax	An integer
x	A real value
result_array	An array of size `lmax`
result_deriv_array	An array of size `lmax`

Returns: The function value

Definition at line 125 of file sf_legendre.hpp.

◆ Pl_e()

int gsl::sf::legendre::Pl_e	(	int const	l,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_Pl_e().

P_l(x) l >= 0; |x| <= 1

Parameters

l	An integer
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 65 of file sf_legendre.hpp.

◆ Plm()

double gsl::sf::legendre::Plm	(	int const	l,
		int const	m,
		double const	x
	)

inline

C++ version of gsl_sf_legendre_Plm().

P_l^m(x) m >= 0; l >= m; |x| <= 1.0

Note that this function grows combinatorially with l. Therefore we can easily generate an overflow for l larger than about 150.

There is no trouble for small m, but when m and l are both large, then there will be trouble. Rather than allow overflows, these functions refuse to calculate when they can sense that l and m are too big.

If you really want to calculate a spherical harmonic, then DO NOT use this. Instead use legendre_sphPlm() below, which uses a similar recursion, but with the normalized functions.

Parameters

l	An integer
m	An integer
x	A real value

Returns: The function value

Definition at line 274 of file sf_legendre.hpp.

◆ Plm_array()

template<typename DATA >

int gsl::sf::legendre::Plm_array	(	int const	lmax,
		int const	m,
		double const	x,
		DATA &	result_array
	)

inline

C++ version of gsl_sf_legendre_Plm_array().

P_l^m(x) m >= 0; l >= m; |x| <= 1.0 l=|m|,...,lmax

Parameters

lmax	An integer
m	An integer
x	A real value
result_array	An array of size `lmax`

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 301 of file sf_legendre.hpp.

◆ Plm_deriv_array()

template<typename DATA >

int gsl::sf::legendre::Plm_deriv_array	(	int const	lmax,
		int const	m,
		double const	x,
		DATA &	result_array,
		DATA &	result_deriv_array
	)

inline

C++ version of gsl_sf_legendre_Plm_deriv_array().

P_l^m(x) and d(P_l^m(x))/dx; m >= 0; lmax >= m; |x| <= 1.0 l=|m|,...,lmax

Parameters

lmax	An integer
m	An integer
x	A real value
result_array	An array of size `lmax`
result_deriv_array	An array of size `lmax`

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 333 of file sf_legendre.hpp.

◆ Plm_e()

int gsl::sf::legendre::Plm_e	(	int const	l,
		int const	m,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_Plm_e().

P_l^m(x) m >= 0; l >= m; |x| <= 1.0

Note that this function grows combinatorially with l. Therefore we can easily generate an overflow for l larger than about 150.

There is no trouble for small m, but when m and l are both large, then there will be trouble. Rather than allow overflows, these functions refuse to calculate when they can sense that l and m are too big.

If you really want to calculate a spherical harmonic, then DO NOT use this. Instead use legendre_sphPlm() below, which uses a similar recursion, but with the normalized functions.

Parameters

l	An integer
m	An integer
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 251 of file sf_legendre.hpp.

◆ Q0()

double gsl::sf::legendre::Q0 ( double const x )

inline

C++ version of gsl_sf_legendre_Q0().

Q_0(x), x > -1, x != 1

Parameters

x	A real value

Returns: The function value

Definition at line 194 of file sf_legendre.hpp.

◆ Q0_e()

int gsl::sf::legendre::Q0_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_Q0_e().

Q_0(x), x > -1, x != 1

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 186 of file sf_legendre.hpp.

◆ Q1()

double gsl::sf::legendre::Q1 ( double const x )

inline

C++ version of gsl_sf_legendre_Q1().

Q_1(x), x > -1, x != 1

Parameters

x	A real value

Returns: The function value

Definition at line 210 of file sf_legendre.hpp.

◆ Q1_e()

int gsl::sf::legendre::Q1_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_Q1_e().

Q_1(x), x > -1, x != 1

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 202 of file sf_legendre.hpp.

◆ Ql()

double gsl::sf::legendre::Ql	(	int const	l,
		double const	x
	)

inline

C++ version of gsl_sf_legendre_Ql().

Q_l(x), x > -1, x != 1, l >= 0

Parameters

l	An integer
x	A real value

Returns: The function value

Definition at line 228 of file sf_legendre.hpp.

◆ Ql_e()

int gsl::sf::legendre::Ql_e	(	int const	l,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_Ql_e().

Q_l(x), x > -1, x != 1, l >= 0

Parameters

l	An integer
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 219 of file sf_legendre.hpp.

◆ SCHMIDT()

legendre_t const gsl::sf::legendre::SCHMIDT ( )

inline

Type.

Returns: GSL_SF_LEGENDRE_SCHMIDT

Definition at line 41 of file sf_legendre.hpp.

◆ SPHARM()

legendre_t const gsl::sf::legendre::SPHARM ( )

inline

Type.

Returns: GSL_SF_LEGENDRE_SPHARM

Definition at line 46 of file sf_legendre.hpp.

◆ sphPlm()

double gsl::sf::legendre::sphPlm	(	int const	l,
		int const	m,
		double const	x
	)

inline

C++ version of gsl_sf_legendre_sphPlm().

P_l^m(x), normalized properly for use in spherical harmonics m >= 0; l >= m; |x| <= 1.0

There is no overflow problem, as there is for the standard normalization of P_l^m(x).

Specifically, it returns:

   sqrt((2l+1)/(4pi)) sqrt((l-m)!/(l+m)!) P_l^m(x)

Parameters

l	An integer
m	An integer
x	A real value

Returns: The function value

Definition at line 374 of file sf_legendre.hpp.

◆ sphPlm_e()

int gsl::sf::legendre::sphPlm_e	(	int const	l,
		int	m,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_legendre_sphPlm_e().

P_l^m(x), normalized properly for use in spherical harmonics m >= 0; l >= m; |x| <= 1.0

There is no overflow problem, as there is for the standard normalization of P_l^m(x).

Specifically, it returns:

   sqrt((2l+1)/(4pi)) sqrt((l-m)!/(l+m)!) P_l^m(x)

Parameters

l	An integer
m	An integer
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 356 of file sf_legendre.hpp.

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ legendre_t

Function Documentation

◆ array()

◆ array_e()

◆ array_index()

◆ array_n()

◆ array_size()

◆ deriv2_alt_array()

◆ deriv2_alt_array_e()

◆ deriv2_array()

◆ deriv2_array_e()

◆ deriv_alt_array()

◆ deriv_alt_array_e()

◆ deriv_array()

◆ deriv_array_e()

◆ FULL()

◆ H3d()

◆ H3d_0()

◆ H3d_0_e()

◆ H3d_1()

◆ H3d_1_e()

◆ H3d_array()

◆ H3d_e()

◆ nlm()

◆ NONE()

◆ P1()

◆ P1_e()

◆ P2()

◆ P2_e()

◆ P3()

◆ P3_e()

◆ Pl()

◆ Pl_array()

◆ Pl_deriv_array()

◆ Pl_e()

◆ Plm()

◆ Plm_array()

◆ Plm_deriv_array()

◆ Plm_e()

◆ Q0()

◆ Q0_e()

◆ Q1()

◆ Q1_e()

◆ Ql()

◆ Ql_e()

◆ SCHMIDT()

◆ SPHARM()

◆ sphPlm()

◆ sphPlm_e()