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    @stdlib/math-base-tools-lucaspoly
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    0.0.6 • Public • Published

    Lucas Polynomial

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    Evaluate a Lucas polynomial.

    A Lucas polynomial is expressed according to the following recurrence relation

    Lucas polynomial.

    Alternatively, if L(n,k) is the coefficient of x^k in L_n(x), then

    Lucas polynomial expressed as a sum.

    We can extend Lucas polynomials to negative n using the identity

    NegaLucas polynomial.

    Installation

    npm install @stdlib/math-base-tools-lucaspoly

    Usage

    var lucaspoly = require( '@stdlib/math-base-tools-lucaspoly' );

    lucaspoly( n, x )

    Evaluates a Lucas polynomial at a value x.

    var v = lucaspoly( 5, 2.0 ); // => 2^5 + 5*2^3 + 5*2
    // returns 82.0

    lucaspoly.factory( n )

    Uses code generation to generate a function for evaluating a Lucas polynomial.

    var polyval = lucaspoly.factory( 5 );
    
    var v = polyval( 1.0 ); // => 1^5 + 5*1^3 + 5
    // returns 11.0
    
    v = polyval( 2.0 ); // => 2^5 + 5*2^3 + 5*2
    // returns 82.0

    Notes

    • For hot code paths, a compiled function will be more performant than lucaspoly().
    • While code generation can boost performance, its use may be problematic in browser contexts enforcing a strict content security policy (CSP). If running in or targeting an environment with a CSP, avoid using code generation.

    Examples

    var lucaspoly = require( '@stdlib/math-base-tools-lucaspoly' );
    
    var i;
    
    // Compute the negaLucas and Lucas numbers...
    for ( i = -76; i < 77; i++ ) {
        console.log( 'L_%d = %d', i, lucaspoly( i, 1.0 ) );
    }

    See Also


    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 © 2016-2022. The Stdlib Authors.

    Install

    npm i @stdlib/math-base-tools-lucaspoly

    Homepage

    stdlib.io

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    Version

    0.0.6

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    Collaborators

    • stdlib-bot
    • kgryte
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    • rreusser