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 uniform = require( '@stdlib/random/array/uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var bessely1 = require( '@stdlib/math/base/special/bessely1' );

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

logEachMap( 'bessely1(%0.4f) = %0.4f', x, bessely1 );

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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.