core/vnl/vnl_bessel.h File Reference

Bessel functions of the first kind. More...

#include <vnl/vnl_vector.h>

Go to the source code of this file.

Functions
double	vnl_bessel (unsigned n, double x)
	Returns J_n(x), the value of the Bessel function of order n at x.
double	vnl_bessel0 (double x)
	Returns J_0(x), the value of the Bessel function of order 0 at x.
void	vnl_bessel (unsigned n_max, double x, vnl_vector< double > &J)
	Compute Bessel functions of first kind up to order n_max.

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Detailed Description

Bessel functions of the first kind.

Author:

Tim Cootes

Definition in file vnl_bessel.h.

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Function Documentation

double vnl_bessel	(	unsigned	n,
		double	x
	)

Returns J_n(x), the value of the Bessel function of order n at x.

Bessel function of the first kind of order n

Bessel function of the first kind of order zero.

Uses recurrence relation: J_(n-1)(x)+J_(n+1)=(2n/x)J_n(x)

Definition at line 69 of file vnl_bessel.cxx.

void vnl_bessel	(	unsigned	n_max,
		double	x,
		vnl_vector< double > &	J
	)

Compute Bessel functions of first kind up to order n_max.

On exit, J[i] = J_i(x) for i=0..n_max

On exit, J[i] = J_i(x) for i=0..n_max

Uses recurrence relation: J_(n-1)(x)+J_(n+1)=(2n/x)J_n(x) Thus J_n(x) = (2(n+1)/x)J_(n+1)(x) - J_(n+2)(x) Start with arbitrary guess for high n and work backwards. Normalise suitably.

Definition at line 17 of file vnl_bessel.cxx.

double vnl_bessel0

(

double

x

)

Returns J_0(x), the value of the Bessel function of order 0 at x.

Bessel function of the first kind of order zero

Bessel function of the first kind of order zero.

Uses recurrence relation: J_(n-1)(x)+J_(n+1)=(2n/x)J_n(x)

Definition at line 45 of file vnl_bessel.cxx.