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

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

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( -1.0 );
// returns NaN

v = y1( Infinity );
// returns 0.0

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 ) );
}