Lucas Polynomial

Evaluate a Lucas polynomial.

A Lucas polynomial is expressed according to the following recurrence relation

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

We can extend Lucas polynomials to negative n using the identity

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

• @stdlib/math-base/tools/evalpoly: evaluate a polynomial using double-precision floating-point arithmetic.
• @stdlib/math-base/tools/fibpoly: evaluate a Fibonacci polynomial.

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.