# LaguerreHalf: Laguerre Polynomial (Half) In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

 LaguerreHalf R Documentation

## 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}{π} \int_0^π \exp(x\cos(θ)) \cos(k θ)\; \mathrm{d}θ\mbox{.}

### Usage

LaguerreHalf(x)


### Arguments

 x A value.

### Value

The value for the Laguerre polynomial is returned.

### Author(s)

W.H. Asquith

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