Contains the code to calculate Legendre polynomials. More...

#include "arts.h"
#include "matpackI.h"

Include dependency graph for legendre.h:

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Functions
Numeric	legendre_poly (Index l, Index m, Numeric x)
	legendre_poly More...

Numeric	legendre_poly_norm_schmidt (Index l, Index m, Numeric x)
	legendre_poly_norm_schmidt More...

Numeric	legendre_poly_deriv (Index l, Index m, Numeric x)
	legendre_poly_deriv More...

Numeric	legendre_poly_norm_schmidt_deriv (Index l, Index m, Numeric x)
	legendre_poly_norm_schmidt_deriv More...

Numeric	g_legendre_poly (Index l, Index m, Numeric x)
	g_legendre_poly More...

Numeric	g_legendre_poly_norm_schmidt (Index l, Index m, Numeric x)
	g_legendre_poly_norm_schmidt More...

Numeric	g_legendre_poly_deriv (Index l, Index m, Numeric x)
	g_legendre_poly_deriv More...

Numeric	g_legendre_poly_norm_schmidt_deriv (Index l, Index m, Numeric x)
	g_legendre_poly_norm_schmidt_deriv More...

Numeric	g_legendre_poly_norm_schmidt_deriv1 (Index l, Index m, Numeric x)
	g_legendre_poly_norm_schmidt_deriv1 More...

Numeric	g_legendre_poly_norm_schmidt_deriv2 (Index l, Index m, Numeric x)
	g_legendre_poly_norm_schmidt_deriv2 More...

Numeric	g_legendre_poly_norm_schmidt_deriv3 (Index l, Index m, Numeric x)
	g_legendre_poly_norm_schmidt_deriv3 More...

Numeric	g_legendre_poly_norm_schmidt_deriv4 (Index l, Index m, Numeric x)
	g_legendre_poly_norm_schmidt_deriv4 More...

Detailed Description

Contains the code to calculate Legendre polynomials.

Author: Oliver Lemke

Date: 2003-08-14

Definition in file legendre.h.

Function Documentation

◆ g_legendre_poly()

Numeric g_legendre_poly	(	Index	l,
		Index	m,
		Numeric	x
	)

g_legendre_poly

Returns the associated Legendre polynomial Plm(x) without the factor (-1)^m.

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| <= 1

The code is based on the Numerical recipes. Results were compared to the Legendre calculations from the GNU Scientific library and found to be identical.

Returns: Plm

Parameters

l	Index
m	Index
x	Value

Author: Nikolay Koulev

Date: 2003-09-02

Definition at line 349 of file legendre.cc.

References abs, and ll.

Referenced by g_legendre_poly_deriv(), g_legendre_poly_norm_schmidt(), g_legendre_poly_norm_schmidt_deriv(), g_legendre_poly_norm_schmidt_deriv1(), g_legendre_poly_norm_schmidt_deriv2(), g_legendre_poly_norm_schmidt_deriv3(), and g_legendre_poly_norm_schmidt_deriv4().

◆ g_legendre_poly_deriv()

Numeric g_legendre_poly_deriv	(	Index	l,
		Index	m,
		Numeric	x
	)

g_legendre_poly_deriv

Returns the derivative of the associated Legendre polynomial Plm(x)) without the factor (-1)^m..

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| < 1

Returns: dPlm

Parameters

l	Index
m	Index
x	Value

Author: Nikolay Koulev

Date: 2003-09-02

Definition at line 458 of file legendre.cc.

References g_legendre_poly().

◆ g_legendre_poly_norm_schmidt()

Numeric g_legendre_poly_norm_schmidt	(	Index	l,
		Index	m,
		Numeric	x
	)

g_legendre_poly_norm_schmidt

Returns the Schmidt quasi-normalized associated Legendre polynomial Plm(x)) without the factor (-1)^m..

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| <= 1

The code is based on the Numerical recipes. Results were compared to the Legendre calculations from the GNU Scientific library and found to be identical.

Returns: Plm

Parameters

l	Index
m	Index
x	Value

Author: Nikolay koulev

Date: 2003-09-02

Definition at line 421 of file legendre.cc.

References fac(), and g_legendre_poly().

Referenced by g_legendre_poly_norm_schmidt_deriv2(), and magfield_nk().

◆ g_legendre_poly_norm_schmidt_deriv()

Numeric g_legendre_poly_norm_schmidt_deriv	(	Index	l,
		Index	m,
		Numeric	x
	)

g_legendre_poly_norm_schmidt_deriv

Returns the derivative of the Schmidt quasi-normalized associated Legendre polynomial Plm(x)) without the factor (-1)^m.

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| < 1

Returns: dPlm

Parameters

l	Index
m	Index
x	Value

Author: Nikolay Koulev

Date: 2003-09-02

Definition at line 543 of file legendre.cc.

References fac(), and g_legendre_poly().

◆ g_legendre_poly_norm_schmidt_deriv1()

Numeric g_legendre_poly_norm_schmidt_deriv1	(	Index	l,
		Index	m,
		Numeric	x
	)

g_legendre_poly_norm_schmidt_deriv1

Returns the derivative of the Schmidt quasi-normalized associated Legendre polynomial Plm(x)) without the factor (-1)^m. Utilizes the simplest recurrence scheme.

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| < 1

Returns: dPlm

Parameters

l	Index
m	Index
x	Value

Author: Nikolay Koulev

Date: 2003-09-02

Definition at line 632 of file legendre.cc.

References fac(), and g_legendre_poly().

◆ g_legendre_poly_norm_schmidt_deriv2()

Numeric g_legendre_poly_norm_schmidt_deriv2	(	Index	l,
		Index	m,
		Numeric	x
	)

g_legendre_poly_norm_schmidt_deriv2

Returns the derivative of the Schmidt quasi-normalized associated Legendre polynomial Plm(x)) without the factor (-1)^m.

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| < 1

Returns: dPlm

Parameters

l	Index
m	Index
x	Value

Author: Nikolay Koulev

Date: 2003-09-02

Definition at line 724 of file legendre.cc.

References fac(), g_legendre_poly(), and g_legendre_poly_norm_schmidt().

◆ g_legendre_poly_norm_schmidt_deriv3()

Numeric g_legendre_poly_norm_schmidt_deriv3	(	Index	l,
		Index	m,
		Numeric	x
	)

g_legendre_poly_norm_schmidt_deriv3

Returns the derivative of the Schmidt quasi-normalized associated Legendre polynomial Plm(x)) without the factor (-1)^m.

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| < 1

Returns: dPlm

Parameters

l	Index
m	Index
x	Value

Author: Nikolay Koulev

Date: 2003-09-02

Definition at line 812 of file legendre.cc.

References fac(), and g_legendre_poly().

Referenced by magfield_nk().

◆ g_legendre_poly_norm_schmidt_deriv4()

Numeric g_legendre_poly_norm_schmidt_deriv4	(	Index	l,
		Index	m,
		Numeric	x
	)

g_legendre_poly_norm_schmidt_deriv4

Returns the derivative of the Schmidt quasi-normalized associated Legendre polynomial Plm(x)) without the factor (-1)^m.

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| < 1

Returns: dPlm

Parameters

l	Index
m	Index
x	Value

Author: Nikolay Koulev

Date: 2003-09-02

Definition at line 900 of file legendre.cc.

References fac(), and g_legendre_poly().

◆ legendre_poly()

Numeric legendre_poly	(	Index	l,
		Index	m,
		Numeric	x
	)

legendre_poly

Returns the associated Legendre polynomial Plm(x).

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| <= 1

The code is based on the Numerical recipes. Results were compared to the Legendre calculations from the GNU Scientific library and found to be identical.

Returns: Plm

Parameters

l	Index
m	Index
x	Value

Author: Oliver Lemke

Date: 2003-08-14

Definition at line 66 of file legendre.cc.

References abs, and ll.

Referenced by legendre_poly_deriv(), legendre_poly_norm_schmidt(), and main().

◆ legendre_poly_deriv()

Numeric legendre_poly_deriv	(	Index	l,
		Index	m,
		Numeric	x
	)

legendre_poly_deriv

Returns the derivative of the associated Legendre polynomial Plm(x).

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| < 1

Returns: dPlm

Parameters

l	Index
m	Index
x	Value

Author: Oliver Lemke

Date: 2003-08-18

Definition at line 173 of file legendre.cc.

References legendre_poly().

Referenced by main().

◆ legendre_poly_norm_schmidt()

Numeric legendre_poly_norm_schmidt	(	Index	l,
		Index	m,
		Numeric	x
	)

legendre_poly_norm_schmidt

Returns the Schmidt quasi-normalized associated Legendre polynomial Plm(x).

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| <= 1

The code is based on the Numerical recipes. Results were compared to the Legendre calculations from the GNU Scientific library and found to be identical.

Returns: Plm

Parameters

l	Index
m	Index
x	Value

Author: Oliver Lemke

Date: 2003-08-15

Definition at line 137 of file legendre.cc.

References fac(), and legendre_poly().

Referenced by legendre_poly_norm_schmidt_deriv(), and main().

◆ legendre_poly_norm_schmidt_deriv()

Numeric legendre_poly_norm_schmidt_deriv	(	Index	l,
		Index	m,
		Numeric	x
	)

legendre_poly_norm_schmidt_deriv

Returns the derivative of the Schmidt quasi-normalized associated Legendre polynomial Plm(x).

The input parameters must fulfill the following conditions: 0 <= m <= l and |x| < 1

Returns: dPlm

Parameters

l	Index
m	Index
x	Value

Author: Nikolay Koulev

Date: 2003-08-18

Definition at line 257 of file legendre.cc.

References fac(), and legendre_poly_norm_schmidt().

Referenced by main().

Functions

Detailed Description

Function Documentation

◆ g_legendre_poly()

◆ g_legendre_poly_deriv()

◆ g_legendre_poly_norm_schmidt()

◆ g_legendre_poly_norm_schmidt_deriv()

◆ g_legendre_poly_norm_schmidt_deriv1()

◆ g_legendre_poly_norm_schmidt_deriv2()

◆ g_legendre_poly_norm_schmidt_deriv3()

◆ g_legendre_poly_norm_schmidt_deriv4()

◆ legendre_poly()

◆ legendre_poly_deriv()

◆ legendre_poly_norm_schmidt()

◆ legendre_poly_norm_schmidt_deriv()