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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
where the parameter m
is related to the modulus k
by m = k^2
.
Installation
npm install @stdlib/math-base-special-ellipe
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): 71–76. doi:10.1016/j.cam.2014.12.038.
See Also
-
@stdlib/math-base/special/ellipj
: compute the Jacobi elliptic functions sn, cn, and dn. -
@stdlib/math-base/special/ellipk
: compute the complete elliptic integral of the first kind.
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.
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