Compute the Bessel function of the second kind of order zero.
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Compute the [Bessel function of the second kind][bessel-second-kind] of order zero.
math
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.bash
npm install @stdlib/math-base-special-bessely0script tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var y0 = require( '@stdlib/math-base-special-bessely0' );x.javascript
var v = y0( 0.0 );
// returns -Infinity
v = y0( 1.0 );
// returns ~0.088
v = y0( Infinity );
// returns 0.0x < 0 or x is NaN, the function returns NaN.javascript
var v = y0( -1.0 );
// returns NaN
v = y0( -Infinity );
// returns NaN
v = y0( NaN );
// returns NaNjavascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var bessely0 = require( '@stdlib/math-base-special-bessely0' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 100, 0.0, 100.0, opts );
logEachMap( 'bessely0(%0.4f) = %0.4f', x, bessely0 );c
#include "stdlib/math/base/special/bessely0.h"x.c
double out = stdlib_base_bessely0( 0.0 );
// returns -Infinity
out = stdlib_base_bessely0( 1.0 );
// returns ~0.088[in] double input value.c
double stdlib_base_bessely0( const double x );c
#include "stdlib/math/base/special/bessely0.h"
#include <stdio.h>
int main( void ) {
const double x[] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
double y;
int i;
for ( i = 0; i < 5; i++ ) {
y = stdlib_base_bessely0( x[ i ] );
printf( "bessely0(%lf) = %lf\n", x[ i ], y );
}
}
