Bessel Functions: _j0, _j1, _jn, _y0, _y1, _yn

Computes the Bessel function of the first or second kind, of orders 0, 1, or n. The Bessel functions are commonly used in the mathematics of electromagnetic wave theory.

Syntax

double _j0(
   double x
);
double _j1(
   double x
);
double _jn(
   int n,
   double x
);
double _y0(
   double x
);
double _y1(
   double x
);
double _yn(
   int n,
   double x
);

Parameters

x
Floating-point value.

n
Integer order of Bessel function.

Return Value

Each of these routines returns a Bessel function of x. If x is negative in the _y0, _y1, or _yn functions, the routine sets errno to EDOM, prints a _DOMAIN error message to stderr, and returns _HUGE_VAL. You can modify error handling by using _matherr.

Remarks

The _j0, _j1, and _jn routines return Bessel functions of the first kind: orders 0, 1, and n, respectively.

Input SEH Exception Matherr Exception
± QNAN, IND INVALID _DOMAIN

The _y0, _y1, and _yn routines return Bessel functions of the second kind: orders 0, 1, and n, respectively.

Input SEH Exception Matherr Exception
± QNAN, IND INVALID _DOMAIN
± 0 ZERODIVIDE _SING
|x| < 0.0 INVALID _DOMAIN

Requirements

Routine Required header
_j0, _j1, _jn, _y0, _y1, _yn <cmath> (C++), <math.h> (C, C++)

For additional compatibility information, see Compatibility.

Example

// crt_bessel1.c
#include <math.h>
#include <stdio.h>

int main( void )
{
   double x = 2.387;
   int n = 3, c;

   printf( "Bessel functions for x = %f:\n", x );
   printf( "   Kind   Order  Function     Result\n\n" );
   printf( "   First  0      _j0( x )     %f\n", _j0( x ) );
   printf( "   First  1      _j1( x )     %f\n", _j1( x ) );
   for( c = 2; c < 5; c++ )
      printf( "   First  %d      _jn( %d, x )  %f\n", c, c, _jn( c, x ) );
   printf( "   Second 0      _y0( x )     %f\n", _y0( x ) );
   printf( "   Second 1      _y1( x )     %f\n", _y1( x ) );
   for( c = 2; c < 5; c++ )
      printf( "   Second %d      _yn( %d, x )  %f\n", c, c, _yn( c, x ) );
}
Bessel functions for x = 2.387000:
   Kind   Order  Function     Result

   First  0      _j0( x )     0.009288
   First  1      _j1( x )     0.522941
   First  2      _jn( 2, x )  0.428870
   First  3      _jn( 3, x )  0.195734
   First  4      _jn( 4, x )  0.063131
   Second 0      _y0( x )     0.511681
   Second 1      _y1( x )     0.094374
   Second 2      _yn( 2, x )  -0.432608
   Second 3      _yn( 3, x )  -0.819314
   Second 4      _yn( 4, x )  -1.626833

See also

Floating-Point Support
_matherr