Bessel function of the first kind, with order one.

Contents

Interface Function Documentation Page Comments

Interface

#include <codecogs/maths/special/bessel/j/j1.h>

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

	double	J1 (double x) Bessel function of the first kind, with order one.
	Real	cc_J1 (Real x) This function is available as a Microsoft Excel add-in.

Function Documentation

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

The domain is divided into the intervals [0, 8] and [8, infinity]. In the first interval a 24 term Chebyshev expansion is used. In the second, the asymptotic trigonometric representation is employed using two rational functions of degree 5/5.

See also Maths/Special/Bessel/J/J

Accuracy:

                         Relative error:
 arithmetic   domain     # trials      peak         rms
     DEC       0, 30       10000       4.0e-17     1.1e-17
     IEEE      0, 30       30000       2.6e-16     1.1e-16
 

Example:

#include <stdio.h>
#include <codecogs/maths/special/bessel/j/j1.h>
int main()
{
  using namespace Maths::Special::Bessel::J;
  for(double x=0; x<6; x+=1)
  {
    double y=J1(x);
    printf("\n J1(%.1lf)=%lf", x,y);
  }
  return 0;
}

Output:

J1(0.0)=0.000000
J1(1.0)=0.440051
J1(2.0)=0.576725
J1(3.0)=0.339059
J1(4.0)=-0.066043
J1(5.0)=-0.327579

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)