A Fibonacci polynomial is expressed according to the following recurrence relation

Alternatively, if F(n,k) is the coefficient of x^k in F_n(x), then

where

We can extend Fibonacci polynomials to negative n using the identity

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch.
• If you are using Deno, visit the deno branch.
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch.

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

Evaluates a Fibonacci polynomial at a value x.

var v = fibpoly( 5, 2.0 ); // => 2^4 + 3*2^2 + 1
// returns 29.0

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

var polyval = fibpoly.factory( 5 );

var v = polyval( 1.0 ); // => 1^4 + 3*1^2 + 1
// returns 5.0

v = polyval( 2.0 ); // => 2^4 + 3*2^2 + 1
// returns 29.0

• For hot code paths, a compiled function will be more performant than fibpoly().
• 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.

• @stdlib/math/base/tools/evalpoly: evaluate a polynomial.
• @stdlib/math/base/tools/lucaspoly: evaluate a Lucas polynomial.

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.

See LICENSE.

Copyright © 2016-2022. The Stdlib Authors.