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

upper Y 0 left-parenthesis x right-parenthesis equals StartFraction 1 Over pi EndFraction integral Subscript 0 Superscript pi Baseline sine left-parenthesis x sine theta right-parenthesis d theta minus StartFraction 2 Over pi EndFraction integral Subscript 0 Superscript normal infinity Baseline e Superscript minus x hyperbolic sine t Baseline d t period

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( -1.0 );
// returns NaN

v = y0( Infinity );
// returns 0.0

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 ) );
}