j0

Compute the Bessel function of the first kind of order zero.

The Bessel function of the first kind of order zero is defined as

$$J_0 (x) = \frac{1}{2 \pi} \int_{-\pi}^\pi e^{- i x \sin(\tau)} \,d\tau.$$

Usage

var j0 = require( '@stdlib/math/base/special/besselj0' );

j0( x )

Computes the Bessel function of the first kind of order zero at x.

var v = j0( 0.0 );
// returns 1.0

v = j0( 1.0 );
// returns ~0.765

v = j0( Infinity );
// returns 0.0

v = j0( -Infinity );
// returns 0.0

v = j0( NaN );
// returns NaN

Examples

var uniform = require( '@stdlib/random/array/uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var besselj0 = require( '@stdlib/math/base/special/besselj0' );

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

logEachMap( 'besselj0(%0.4f) = %0.4f', x, besselj0 );

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C APIs

Usage

#include "stdlib/math/base/special/besselj0.h"

stdlib_base_besselj0( x )

Computes the Bessel function of the first kind of order zero at x.

double out = stdlib_base_besselj0( 0.0 );
// returns 1.0

out = stdlib_base_besselj0( 1.0 );
// returns ~0.765

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_besselj0( const double x );

Examples

#include "stdlib/math/base/special/besselj0.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_besselj0( x[ i ] );
        printf( "besselj0(%lf) = %lf\n", x[ i ], y );
    }
}

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See Also

• @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.
• @stdlib/math/base/special/bessely1: compute the Bessel function of the second kind of order one.