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Bessel Functions 

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.

// 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 ) );
}

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( 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

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