Generalized Laguerre polynomial

LaguerreGen calculates the generalized Laguerre polynomial L{n, alpha} for real valued alphas

LaguerreGen calculates the generalized Laguerre polynomial L{n, alpha}

This function computes the generalized Laguerre polynomial L{n,alpha}.
If no alpha is supplied, alpha is set to zero and this function calculates the "normal" Laguerre polynomial.

Input:
- n = nonnegative integer as degree level
- alpha >= -1 real number (input is optional)

The output is formated as a polynomial vector of degree (n+1) corresponding to MATLAB norms (that is the highest coefficient is the first element).

Possible usage:
- polyval(LaguerreGen(n, alpha), x) evaluates L{n, alpha}(x)
- roots(LaguerreGen(n, alpha)) calculates roots of L{n, alpha}

Calculation is done recursively using matrix operations for very fast execution time. The formula is taken from Szegö: Orthogonal Polynomials, 1958, formula (5.1.10)