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

Installation

npm install @stdlib/math-base-special-bessely0

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 uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var bessely0 = require( '@stdlib/math-base-special-bessely0' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 100, 0.0, 100.0, opts );

logEachMap( 'bessely0(%0.4f) = %0.4f', x, bessely0 );

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 );
    }
}

See Also

• @stdlib/math-base/special/besselj0: compute the Bessel function of the first kind of order zero.
• @stdlib/math-base/special/besselj1: compute the Bessel function of the first kind of order one.
• @stdlib/math-base/special/bessely1: compute the Bessel function of the second kind of order one.

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

Copyright

Copyright © 2016-2026. The Stdlib Authors.