SphericalBessel Namespace Reference

Detailed Description

Wrappers for returning Spherical Bessel functions.

Has an "exact" version, and a faster approx version (good to ~ 1.e-9)

Classes
class	JL_table
	Spherical Bessel Lookup table; in the form j_L(qr) = J[L][q][r]. More...

Functions
double	jL (int L, double x)
	Spherical Bessel function; uses low-x approximation where appropriate.
double	exactGSL_JL (int L, double x)
	Spherical Bessel function of first kind via GSL.
double	exactGSL_YL (int L, double x)
	Spherical Bessel functions of second kind.
double	yL (int L, double x)
	Used for frequency-dependent Breit - more generic formula that can be used to evaluate spherical Bessel function of second kind for negative orders.
double	PhiL (int L, double x, bool tilde=false)
	Phi_L(x) = [(2L+1)!! / x^L] * j_L(x). If tilde=true, returns 1 - Phi_L(x)
double	PsiL (int L, double x, bool tilde=false)
	Psi_L(x) = [x^{L+1} / (2L-1)!!] * y_L(x). If tilde=true, returns 1 - Psi_L(x)
std::vector< double >	fillBesselVec (int l, const std::vector< double > &xvec)
	Spherical Bessel functions of second kind.
std::vector< double >	fillBesselVec_kr (int l, double k, const std::vector< double > &rvec)
void	fillBesselVec_kr (int l, double k, const std::vector< double > &r, std::vector< double > *jl)

Function Documentation

jL()

double SphericalBessel::jL	(	int	L,
		double	x
	)

Spherical Bessel function; uses low-x approximation where appropriate.

exactGSL_JL()

double SphericalBessel::exactGSL_JL	(	int	L,
		double	x
	)

Spherical Bessel function of first kind via GSL.

exactGSL_YL()

double SphericalBessel::exactGSL_YL	(	int	L,
		double	x
	)

Spherical Bessel functions of second kind.

yL()

double SphericalBessel::yL	(	int	L,
		double	x
	)

Used for frequency-dependent Breit - more generic formula that can be used to evaluate spherical Bessel function of second kind for negative orders.

Spherical Bessel function of second kind, y_L(x)

PhiL()

double SphericalBessel::PhiL	(	int	L,
		double	x,
		bool	tilde
	)

Phi_L(x) = [(2L+1)!! / x^L] * j_L(x). If tilde=true, returns 1 - Phi_L(x)

PsiL()

double SphericalBessel::PsiL	(	int	L,
		double	x,
		bool	tilde
	)

Psi_L(x) = [x^{L+1} / (2L-1)!!] * y_L(x). If tilde=true, returns 1 - Psi_L(x)

fillBesselVec()

std::vector< double > SphericalBessel::fillBesselVec	(	int	l,
		const std::vector< double > &	xvec
	)

Spherical Bessel functions of second kind.

Creates a vector of Jl(r) for given r