bessel-functions-j0-j1-jn-y0-y1-yn.md

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Bessel Functions: _j0, _j1, _jn, _y0, _y1, _yn | Microsoft Docs		11/04/2016			cpp-standard-libraries		article	_j0 _j1 _jn _y0 _y1 _yn	msvcrt.dll msvcr80.dll msvcr90.dll msvcr100.dll msvcr100_clr0400.dll msvcr110.dll msvcr110_clr0400.dll msvcr120.dll msvcr120_clr0400.dll ucrtbase.dll api-ms-win-crt-math-l1-1-0.dll	DLLExport	c.bessel _j0 _j1 _jn _y0 _y1 _yn	C++	Bessel functions _j0 function _j1 function _jn function _y0 function _y1 function _yn function	a21a8bf1-df9d-4ba0-a8c2-e7ef71921d96	14	corob-msft	corob	ghogen

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  

See Also

Floating-Point Support
_matherr