@stdlib/math-base-special-ellipk
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    ellipk

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    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.

    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 ) );
    }

    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.

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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2021. The Stdlib Authors.

    Install

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

    Homepage

    stdlib.io

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    0.0.5

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