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

description	title	ms.date	api_name	api_location	api_type	topic_type	f1_keywords	helpviewer_keywords	ms.assetid
Learn more about: Bessel Functions: _j0, _j1, _jn, _y0, _y1, _yn	Bessel Functions: _j0, _j1, _jn, _y0, _y1, _yn	4/2/2020	_j0 _j1 _jn _y0 _y1 _yn _o__j0 _o__j1 _o__jn _o__y0 _o__y1 _o__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	apiref	c.bessel _j0 _j1 _jn _y0 _y1 _yn	Bessel functions _j0 function _j1 function _jn function _y0 function _y1 function _yn function	a21a8bf1-df9d-4ba0-a8c2-e7ef71921d96

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`

By default, this function's global state is scoped to the application. To change this behavior, see Global state in the CRT.

Requirements

Routine	Required header
_j0, _j1, _jn, _y0, _y1, _yn	<cmath> (C++), <math.h> (C, C++)

For more compatibility information, see Compatibility.

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

Math and floating-point support
_matherr