time-to-botec/js/node_modules/@stdlib/math/base/special/ellipe
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Necessary in order to clearly see the squiggle hotwiring.
2022-12-03 12:44:49 +00:00
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ellipe

Compute the complete elliptic integral of the second kind.

The complete elliptic integral of the second kind is defined as

Complete elliptic integral of the second kind.

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

Usage

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

ellipe( m )

Computes the complete elliptic integral of the second kind.

var v = ellipe( 0.5 );
// returns ~1.351

v = ellipe( -1.0 );
// returns ~1.910

v = ellipe( 2.0 );
// returns NaN

v = ellipe( Infinity );
// returns NaN

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

v = ellipe( NaN );
// returns NaN

Notes

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

Examples

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

var m;
var i;

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