Bessel function of the first kind, with order zero and exponential scaling.

Contents

Interface Function Documentation Page Comments

Interface

#include <codecogs/maths/special/bessel/j/j0.h>

using namespace Maths::Special::Bessel::J;

	double	J0 (double x) Bessel function of the first kind, with order zero and exponential scaling.
	Real	cc_J0 (Real x) This function is available as a Microsoft Excel add-in.

Function Documentation

Returns modified Bessel function of the first kind, with order zero.

The domain is divided into the intervals [0, 5] and [5, infinity]. In the first interval the following rational approximation is used:

where and the two r's are roots of the function.

In the second interval, the Hankel asymptotic expansion is employed with two rational functions of degree 6/6 and 7/7.

See also Maths/Special/Bessel/J/J

Accuracy:

                       Absolute error:
 arithmetic   domain     # trials      peak         rms
    DEC       0, 30       10000       4.4e-17     6.3e-18
    IEEE      0, 30       60000       4.2e-16     1.1e-16
 

Example:

#include <stdio.h>
#include <codecogs/maths/special/bessel/j/j0.h>
int main()
{
 using namespace Maths::Special::Bessel::J;
  for(double x=0; x<6; x+=1)
  {
    double y=J0(x);
    printf("\n J0(%.1lf)=%lf", x,y);
  }
  return 0;
}

Output:

J0(0.0)=1.000000
J0(1.0)=0.765198
J0(2.0)=0.223891
J0(3.0)=-0.260052
J0(4.0)=-0.397150
J0(5.0)=-0.177597

References:

Cephes Math Library Release 2.8: June, 2000

Parameters:

x	input argument

Authors:

Stephen L. Moshier. Copyright 1984, 1987, 2000
Documentation by Will Bateman (August 2005)