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

$$Y_0(x) = \frac{1}{\pi} \int_0^\pi \sin(x \sin\theta) \, d\theta -\frac{2}{\pi} \int_0^\infty e^{-x \sinh t} \, dt.$$

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 ) );
}

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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.