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# Bessel Functions

Visual Studio 2008

The Bessel functions are commonly used in the mathematics of electromagnetic wave theory.

_j0, _j1, _jn

These routines return Bessel functions of the first kind: orders 0, 1, and n, respectively.

_y0, _y1, _yn

These routines return Bessel functions of the second kind: orders 0, 1, and n, respectively.

## 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