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 |
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