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

Article
06/05/2017

The new home for Visual Studio documentation is Visual Studio 2017 Documentation on docs.microsoft.com.

The latest version of this topic can be found at 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 in the Introduction.

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

Share via