@stdlib/math-base-special-ellipk NPM

ellipk

$NPM version$ $Build Status$ $Coverage Status$

Compute the complete elliptic integral of the first kind.

The complete elliptic integral of the first kind is defined as

where the parameter m is related to the modulus k by m = k^2.

Installation

npm install @stdlib/math-base-special-ellipk

Usage

var ellipk = require( '@stdlib/math-base-special-ellipk' );

ellipk( m )

Computes the complete elliptic integral of the first kind.

var v = ellipk( 0.5 );
// returns ~1.854

v = ellipk( -1.0 );
// returns ~1.311

v = ellipk( 2.0 );
// returns NaN

v = ellipk( Infinity );
// returns NaN

v = ellipk( -Infinity );
// returns NaN

v = ellipk( NaN );
// returns NaN

Notes

This function is valid for -∞ < m <= 1.

Examples

var randu = require( '@stdlib/random-base-randu' );
var ellipk = require( '@stdlib/math-base-special-ellipk' );

var m;
var i;

for ( i = 0; i < 100; i++ ) {
    m = -1.0 + ( randu() * 2.0 );
    console.log( 'ellipk(%d) = %d', m, ellipk( m ) );
}

C APIs

Usage

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

stdlib_base_ellipk( m )

Computes the complete elliptic integral of the first kind.

double out = stdlib_base_ellipk( 0.5 );
// returns ~1.854

out = stdlib_base_ellipk( -1.0 );
// returns ~1.311

The function accepts the following arguments:

x: [in] double input value.

double stdlib_base_ellipk( const double m );

Examples

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

int main( void ) {
    double m;
    double v;
    int i;
    
    for ( i = 0; i < 100; i++ ) {
        m = -1.0 + ( ( (double)rand() / (double)RAND_MAX ) * 2.0 );
        v = stdlib_base_ellipk( m );
        printf( "ellipk(%lf) = %lf\n", m, v );
    }
}

References

Fukushima, Toshio. 2009. "Fast computation of complete elliptic integrals and Jacobian elliptic functions." Celestial Mechanics and Dynamical Astronomy 105 (4): 305. doi:10.1007/s10569-009-9228-z.
Fukushima, Toshio. 2015. "Precise and fast computation of complete elliptic integrals by piecewise minimax rational function approximation." Journal of Computational and Applied Mathematics 282 (July): 71–76. doi:10.1016/j.cam.2014.12.038.

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.