y1

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

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

$$Y_1(x) = \frac{1}{\pi} \int_0^\pi \sin(x \sin\theta - \theta) \, d\theta -\frac{1}{\pi} \int_0^\infty \left[ e^t - e^{-t} \right] e^{-x \sinh t} \, dt$$

Usage

var y1 = require( '@stdlib/math/base/special/bessely1' );

y1( x )

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

var v = y1( 0.0 );
// returns -Infinity

v = y1( 1.0 );
// returns ~-0.781

v = y1( Infinity );
// returns 0.0

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

var v = y1( -1.0 );
// returns NaN

v = y1( -Infinity );
// returns NaN

v = y1( NaN );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var y1 = require( '@stdlib/math/base/special/bessely1' );

var x;
var i;

for ( i = 0; i < 100; i++ ) {
    x = randu() * 10.0;
    console.log( 'y1(%d) = %d', x, y1( 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/bessely0: compute the Bessel function of the second kind of order zero.