Evaluate a Lucas polynomial.
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> 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
``bash`
npm install @stdlib/math-base-tools-lucaspoly
`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 + 52^3 + 52
// 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 + 52^3 + 52
// returns 82.0
`
- 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.
`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 ) );
}
`
*
- [@stdlib/math-base/tools/evalpoly][@stdlib/math/base/tools/evalpoly]: evaluate a polynomial using double-precision floating-point arithmetic.
- [@stdlib/math-base/tools/fibpoly][@stdlib/math/base/tools/fibpoly]: evaluate a Fibonacci polynomial.
*
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For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
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---
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