time-to-botec/js/node_modules/@stdlib/math/base/special/ellipk
NunoSempere b6addc7f05 feat: add the node modules
Necessary in order to clearly see the squiggle hotwiring.
2022-12-03 12:44:49 +00:00
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ellipk

Compute the complete elliptic integral of the first kind.

The complete elliptic integral of the first kind is defined as

Complete elliptic integral of the first kind

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

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 ) );
}

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): 7176. doi:10.1016/j.cam.2014.12.038.