This function computes the Laguerre polynomial, which is useful in applications involving the variance of the Rice distribution (see parrice). The Laguerre polynomial is
$$
L_{1/2}(x) = \exp^{x/2}\times[(1-x)I_0(-x/2) - xI_1(-x/2)]\mbox{,}
$$
where the modified Bessel function of the first kind is \(I_k(x)\), which has an R implementation in besselI, and for strictly integer \(k\) is defined as
$$I_k(x) = \frac{1}{\pi} \int_0^\pi \exp(x\cos(\theta)) \cos(k \theta)\; \mathrm{d}\theta\mbox{.}$$