# Fibonacci Polynomial
> Evaluate a [Fibonacci polynomial][fibonacci-polynomials].
A [Fibonacci polynomial][fibonacci-polynomials] 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][fibonacci-polynomials] to negative `n` using the identity
## Usage
```javascript
var fibpoly = require( '@stdlib/math/base/tools/fibpoly' );
```
#### fibpoly( n, x )
Evaluates a [Fibonacci polynomial][fibonacci-polynomials] at a value `x`.
```javascript
var v = fibpoly( 5, 2.0 ); // => 2^4 + 3*2^2 + 1
// returns 29.0
```
#### fibpoly.factory( n )
Uses code generation to generate a `function` for evaluating a [Fibonacci polynomial][fibonacci-polynomials].
```javascript
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
```
## Notes
- 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][mdn-csp] (CSP). If running in or targeting an environment with a CSP, avoid using code generation.
## Examples
```javascript
var fibpoly = require( '@stdlib/math/base/tools/fibpoly' );
var i;
// Compute the negaFibonacci and Fibonacci numbers...
for ( i = -77; i < 78; i++ ) {
console.log( 'F_%d = %d', i, fibpoly( i, 1.0 ) );
}
```
[fibonacci-polynomials]: https://en.wikipedia.org/wiki/Fibonacci_polynomials
[mdn-csp]: https://developer.mozilla.org/en-US/docs/Web/HTTP/CSP
