# Bessel Functions: _y0, _y1, _yn

Visual Studio 6.0

Compute the Bessel function.

double _y0( double x );

double _y1( double x );

double _yn( int n, double x );

 Routine Required Header Compatibility _y0 Win 95, Win NT _y1 Win 95, Win NT _yn Win 95, Win NT

For additional compatibility information, see Compatibility in the Introduction.

Libraries

 LIBC.LIB Single thread static library, retail version LIBCMT.LIB Multithread static library, retail version MSVCRT.LIB Import library for MSVCRT.DLL, retail version

Return Value

Each of these routines returns a Bessel function of x. If x is negative, 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.

Parameters

x

Floating-point value

n

Integer order of Bessel function

Remarks

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

Example

``````/* BESSEL.C: This program illustrates Bessel functions,
* including:    _j0   _j1   _jn   _y0   _y1   _yn
*/

#include <math.h>
#include <stdio.h>

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

printf( "Bessel functions for x = %f:\n", x );
printf( " Kind\t\tOrder\tFunction\tResult\n\n" );
printf( " First\t\t0\t_j0( x )\t%f\n", _j0( x ) );
printf( " First\t\t1\t_j1( x )\t%f\n", _j1( x ) );
for( c = 2; c < 5; c++ )
printf( " First\t\t%d\t_jn( n, x )\t%f\n", c, _jn( c, x ) );
printf( " Second\t0\t_y0( x )\t%f\n", _y0( x ) );
printf( " Second\t1\t_y1( x )\t%f\n", _y1( x ) );
for( c = 2; c < 5; c++ )
printf( " Second\t%d\t_yn( n, x )\t%f\n", c, _yn( c, x ) );
}

``````

Output

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

``````