README.md

j1

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

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

$$J_1 (x) = \frac{1}{2 \pi} \int_{-\pi}^\pi e^{i(\tau - x \sin(\tau))} \,d\tau$$

Usage

var j1 = require( '@stdlib/math/base/special/besselj1' );

j1( x )

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

var v = j1( 0.0 );
// returns 0.0

v = j1( 1.0 );
// returns ~0.440

v = j1( Infinity );
// returns 0.0

v = j1( -Infinity );
// returns 0.0

v = j1( NaN );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var j1 = require( '@stdlib/math/base/special/besselj1' );

var x;
var i;

for ( i = 0; i < 100; i++ ) {
    x = randu() * 10.0;
    console.log( 'j1(%d) = %d', x, j1( x ) );
}

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C APIs

Usage

#include "stdlib/math/base/special/j1.h"

stdlib_base_j1( x )

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

double out = stdlib_base_j1( 0.0 );
// returns 0.0

out = stdlib_base_j1( 1.0 );
// returns ~0.440

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_j1( const double x );

Examples

#include "stdlib/math/base/special/j1.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 0.0, 0.005, 3.14, 10.0, 51.125, 99.99, 100.0 };
    double v;
    int i;
    
    for ( i = 0; i < 7; i++ ) {
        v = stdlib_base_j1( x[ i ] );
        printf( "j1(%lf) = %lf\n", x[ i ], v );
    }
}

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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/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.