LaguerreHalf {lmomco}

Laguerre Polynomial (Half)

Description

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{.}

Usage

LaguerreHalf(x)

Arguments

x

A value.

Value

The value for the Laguerre polynomial is returned.

Author(s)

W.H. Asquith

See Also

pdfrice

Examples

LaguerreHalf(-100^2/(2*10^2))