y0

Compute the Bessel function of the second kind of order zero.

The Bessel function of the second kind of order zero is defined as

Usage

var y0 = require( '@stdlib/math/base/special/bessely0' );

y0( x )

Computes the Bessel function of the second kind of order zero at x.

var v = y0( 0.0 );
// returns -Infinity

v = y0( 1.0 );
// returns ~0.088

v = y0( Infinity );
// returns 0.0

If x < 0 or x is NaN, the function returns NaN.

var v = y0( -1.0 );
// returns NaN

v = y0( -Infinity );
// returns NaN

v = y0( NaN );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var y0 = require( '@stdlib/math/base/special/bessely0' );

var x;
var i;

for ( i = 0; i < 100; i++ ) {
    x = randu() * 10.0;
    console.log( 'y0(%d) = %d', x, y0( x ) );
}

C APIs

Usage

#include "stdlib/math/base/special/bessely0.h"

stdlib_base_bessely0( x )

Computes the Bessel function of the second kind of order zero at x.

double out = stdlib_base_bessely0( 0.0 );
// returns -Infinity

out = stdlib_base_bessely0( 1.0 );
// returns ~0.088

The function accepts the following arguments:

x: [in] double input value.

double stdlib_base_bessely0( const double x );

Examples

#include "stdlib/math/base/special/bessely0.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 0.0, 1.0, 2.0, 3.0, 4.0 };

    double y;
    int i;
    for ( i = 0; i < 5; i++ ) {
        y = stdlib_base_bessely0( x[ i ] );
        printf( "bessely0(%lf) = %lf\n", x[ i ], y );
    }
}