# Lucas Polynomial
> Evaluate a [Lucas polynomial][fibonacci-polynomials].
A [Lucas polynomial][fibonacci-polynomials] 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][fibonacci-polynomials] to negative `n` using the identity
## Usage
```javascript
var lucaspoly = require( '@stdlib/math/base/tools/lucaspoly' );
```
#### lucaspoly( n, x )
Evaluates a [Lucas polynomial][fibonacci-polynomials] at a value `x`.
```javascript
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][fibonacci-polynomials].
```javascript
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][mdn-csp] (CSP). If running in or targeting an environment with a CSP, avoid using code generation.
## Examples
```javascript
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 ) );
}
```
[fibonacci-polynomials]: https://en.wikipedia.org/wiki/Fibonacci_polynomials
[mdn-csp]: https://developer.mozilla.org/en-US/docs/Web/HTTP/CSP
