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Legendre Struct Reference

Evaluate Legendre functions of integer, half integer and non-integer order. More...

#include <Legendre.h>

List of all members.

Static Public Member Functions

double P1 (const double x)
 Evaluate the P1 function.

Dpair P1Err (const double x)
 Evaluate the P1 function and estimate the error.

double P2 (const double x)
 Evaluate the P2 function.

Dpair P2Err (const double x)
 Evaluate the P2 function and estimate the error.

double P3 (const double x)
 Evaluate the P3 function.

Dpair P3Err (const double x)
 Evaluate the P3 function and estimate the error.

double Pl (const int l, const double x)
 Evaluate the Pl function.

Dpair PlErr (const int l, const double x)
 Evaluate the Pl function and estimate the error.

Dvector PlArray (const int lmax, const double x)
 Evaluate the Pl functions for l = 0,...,lmax.

Dvector PlErrArray (const int lmax, const double x)
 Evaluate the Pl function for l = 0...lmax (For now, a clone of PlArray).

double Q0 (const double x)
 Evaluate the Q0 function.

Dpair Q0Err (const double x)
 Evaluate the Q0 function and estimate the error.

double Q1 (const double x)
 Evaluate the Q1 function.

Dpair Q1Err (const double x)
 Evaluate the Q1 function and estimate the error.

double Ql (const int l, const double x)
 Evaluate the Ql function.

Dpair QlErr (const int l, const double x)
 Evaluate the Ql function and estimate the error.

double Plm (const int l, const int m, const double x)
 Evaluate the Plm function.

Dpair PlmErr (const int l, const int m, const double x)
 Evaluate the Plm function and estimate the error.

Dvector PlmArray (const int lmax, const int m, const double x)
 Evaluate the Plm functions for fixed m and l=m,m+1,...,lmax.

double SphericalPlm (const int l, const int m, const double x)
 Evaluate the Spherical Plm function.

Dpair SphericalPlmErr (const int l, const int m, const double x)
 Evaluate the Spherical Plm function and estimate the error.

Dvector SphericalPlmArray (const int lmax, const int m, const double x)
 Evaluate the Spherical Plm functions for fixed m and l=m,m+1,...,lmax.

Dvector SphericalPlmErrArray (const int lmax, const int m, const double x)
 Evaluate the Spherical Plm functions for fixed m and l=m,m+1,...,lmax.

double RegularSphericalConical (const double lambda, double x)
 Evaluate the Regular Spherical Conical function.

Dpair RegularSphericalConicalErr (const double lambda, const double x)
 Evaluate the Regular Spherical Conical function and estimate the error.

double IrregularSphericalConical (const double lambda, const double x)
 Evaluate the Irregular Spherical Conical function.

Dpair IrregularSphericalConicalErr (const double lambda, const double x)
 Evaluate the Irregular Spherical Conical function and estimate the error.

double ConicalP0 (const double lambda, const double x)
 Evaluate the Conical P0 function.

Dpair ConicalP0Err (const double lambda, const double x)
 Evaluate the Conical P0 function and estimate the error.

double ConicalP1 (const double lambda, const double x)
 Evaluate the Conical P1 function.

Dpair ConicalP1Err (const double lambda, const double x)
 Evaluate the Conical P1 function and estimate the error.

double RegularSphericalConicalPl (const int l, const double lambda, const double x)
 Evaluate the Regular Spherical Conical Pl function.

Dpair RegularSphericalConicalPlErr (const int l, const double lambda, const double x)
 Evaluate the Regular Spherical Conical Pl function and estimate the error.

double RegularCylindricalConicalPl (const int l, const double lambda, const double x)
 Evaluate the Regular Cylindrical Conical Pl function.

Dpair RegularCylindricalConicalPlErr (const int l, const double lambda, const double x)
 Evaluate the Regular Cylindrical Conical Pl function and estimate the error.

double H3d0 (const double lambda, const double eta)
 Evaluate the zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

Dpair H3d0Err (const double lambda, const double eta)
 Evaluate the zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space and estimate the error.

double H3d1 (const double lambda, const double eta)
 Evaluate the first radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

Dpair H3d1Err (const double lambda, const double eta)
 Evaluate the first radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space and estimate the error.

double H3dl (const int l, const double lambda, const double eta)
 Evaluate the lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

Dpair H3dlErr (const int l, const double lambda, const double eta)
 Evaluate the lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space and estimate the error.

Dvector H3dlArray (const int lmax, const double lambda, const double eta)
 Evaluate the first l radial eigenfunctions functions for l = 0,...,lmax.

Dvector H3dlErrArray (const int lmax, const double lambda, const double eta)
 Evaluate the first l radial eigenfunctions functions for l = 0,...,lmax and estimate the error. (For now, a clone of H3dlArray).

Detailed Description

Evaluate Legendre functions of integer, half integer and non-integer order.

Definition at line 27 of file Legendre.h.

Member Function Documentation

double Legendre::ConicalP0 (  const double  lambda,
const double  x
)  [static]
 

Evaluate the Conical P0 function.

Dpair Legendre::ConicalP0Err (  const double  lambda,
const double  x
)  [static]
 

Evaluate the Conical P0 function and estimate the error.

double Legendre::ConicalP1 (  const double  lambda,
const double  x
)  [static]
 

Evaluate the Conical P1 function.

Dpair Legendre::ConicalP1Err (  const double  lambda,
const double  x
)  [static]
 

Evaluate the Conical P1 function and estimate the error.

double Legendre::H3d0 (  const double  lambda,
const double  eta
)  [static]
 

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

Dpair Legendre::H3d0Err (  const double  lambda,
const double  eta
)  [static]
 

Evaluate the zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space and estimate the error.

double Legendre::H3d1 (  const double  lambda,
const double  eta
)  [static]
 

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

Dpair Legendre::H3d1Err (  const double  lambda,
const double  eta
)  [static]
 

Evaluate the first radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space and estimate the error.

double Legendre::H3dl (  const int  l,
const double  lambda,
const double  eta
)  [static]
 

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

Dvector Legendre::H3dlArray (  const int  lmax,
const double  lambda,
const double  eta
)  [static]
 

Evaluate the first l radial eigenfunctions functions for l = 0,...,lmax.

Dpair Legendre::H3dlErr (  const int  l,
const double  lambda,
const double  eta
)  [static]
 

Evaluate the lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space and estimate the error.

Dvector Legendre::H3dlErrArray (  const int  lmax,
const double  lambda,
const double  eta
)  [static]
 

Evaluate the first l radial eigenfunctions functions for l = 0,...,lmax and estimate the error. (For now, a clone of H3dlArray).

double Legendre::IrregularSphericalConical (  const double  lambda,
const double  x
)  [static]
 

Evaluate the Irregular Spherical Conical function.

Dpair Legendre::IrregularSphericalConicalErr (  const double  lambda,
const double  x
)  [static]
 

Evaluate the Irregular Spherical Conical function and estimate the error.

double Legendre::P1 (  const double  x  )  [static]
 

Evaluate the P1 function.

Dpair Legendre::P1Err (  const double  x  )  [static]
 

Evaluate the P1 function and estimate the error.

double Legendre::P2 (  const double  x  )  [static]
 

Evaluate the P2 function.

Dpair Legendre::P2Err (  const double  x  )  [static]
 

Evaluate the P2 function and estimate the error.

double Legendre::P3 (  const double  x  )  [static]
 

Evaluate the P3 function.

Dpair Legendre::P3Err (  const double  x  )  [static]
 

Evaluate the P3 function and estimate the error.

double Legendre::Pl (  const int  l,
const double  x
)  [static]
 

Evaluate the Pl function.

Dvector Legendre::PlArray (  const int  lmax,
const double  x
)  [static]
 

Evaluate the Pl functions for l = 0,...,lmax.

Dpair Legendre::PlErr (  const int  l,
const double  x
)  [static]
 

Evaluate the Pl function and estimate the error.

Dvector Legendre::PlErrArray (  const int  lmax,
const double  x
)  [static]
 

Evaluate the Pl function for l = 0...lmax (For now, a clone of PlArray).

double Legendre::Plm (  const int  l,
const int  m,
const double  x
)  [static]
 

Evaluate the Plm function.

Dvector Legendre::PlmArray (  const int  lmax,
const int  m,
const double  x
)  [static]
 

Evaluate the Plm functions for fixed m and l=m,m+1,...,lmax.

Dpair Legendre::PlmErr (  const int  l,
const int  m,
const double  x
)  [static]
 

Evaluate the Plm function and estimate the error.

double Legendre::Q0 (  const double  x  )  [static]
 

Evaluate the Q0 function.

Dpair Legendre::Q0Err (  const double  x  )  [static]
 

Evaluate the Q0 function and estimate the error.

double Legendre::Q1 (  const double  x  )  [static]
 

Evaluate the Q1 function.

Dpair Legendre::Q1Err (  const double  x  )  [static]
 

Evaluate the Q1 function and estimate the error.

double Legendre::Ql (  const int  l,
const double  x
)  [static]
 

Evaluate the Ql function.

Dpair Legendre::QlErr (  const int  l,
const double  x
)  [static]
 

Evaluate the Ql function and estimate the error.

double Legendre::RegularCylindricalConicalPl (  const int  l,
const double  lambda,
const double  x
)  [static]
 

Evaluate the Regular Cylindrical Conical Pl function.

Dpair Legendre::RegularCylindricalConicalPlErr (  const int  l,
const double  lambda,
const double  x
)  [static]
 

Evaluate the Regular Cylindrical Conical Pl function and estimate the error.

double Legendre::RegularSphericalConical (  const double  lambda,
double  x
)  [static]
 

Evaluate the Regular Spherical Conical function.

Dpair Legendre::RegularSphericalConicalErr (  const double  lambda,
const double  x
)  [static]
 

Evaluate the Regular Spherical Conical function and estimate the error.

double Legendre::RegularSphericalConicalPl (  const int  l,
const double  lambda,
const double  x
)  [static]
 

Evaluate the Regular Spherical Conical Pl function.

Dpair Legendre::RegularSphericalConicalPlErr (  const int  l,
const double  lambda,
const double  x
)  [static]
 

Evaluate the Regular Spherical Conical Pl function and estimate the error.

double Legendre::SphericalPlm (  const int  l,
const int  m,
const double  x
)  [static]
 

Evaluate the Spherical Plm function.

Dvector Legendre::SphericalPlmArray (  const int  lmax,
const int  m,
const double  x
)  [static]
 

Evaluate the Spherical Plm functions for fixed m and l=m,m+1,...,lmax.

Dpair Legendre::SphericalPlmErr (  const int  l,
const int  m,
const double  x
)  [static]
 

Evaluate the Spherical Plm function and estimate the error.

Dvector Legendre::SphericalPlmErrArray (  const int  lmax,
const int  m,
const double  x
)  [static]
 

Evaluate the Spherical Plm functions for fixed m and l=m,m+1,...,lmax.

Evaluate the Spherical Plm functions for fixed m and l=m,m+1,...,lmax and estimate the errors. (For now, a clone of SphericalPlmArray)

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