g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_prob_landau (g01etc)

## 1  Purpose

nag_prob_landau (g01etc) returns the value of the Landau distribution function $\Phi \left(\lambda \right)$.

## 2  Specification

 #include #include
 double nag_prob_landau (double x)

## 3  Description

nag_prob_landau (g01etc) evaluates an approximation to the Landau distribution function $\Phi \left(\lambda \right)$ given by
 $Φλ=∫-∞λϕλdλ,$
where $\varphi \left(\lambda \right)$ is described in nag_prob_density_landau (g01mtc), using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).

## 4  References

Kölbig K S and Schorr B (1984) A program package for the Landau distribution Comp. Phys. Comm. 31 97–111

## 5  Arguments

1:     xdoubleInput
On entry: the argument $\lambda$ of the function.

None.

## 7  Accuracy

At least $7$ significant digits are usually correct, but occasionally only $6$. Such accuracy is normally considered to be adequate for applications in experimental physics.
Because of the asymptotic behaviour of $\Phi \left(\lambda \right)$, which is of the order of $\mathrm{exp}\left[-\mathrm{exp}\left(-\lambda \right)\right]$, underflow may occur on some machines when $\lambda$ is moderately large and negative.

None.

## 9  Example

This example evaluates $\Phi \left(\lambda \right)$ at $\lambda =0.5$, and prints the results.

### 9.1  Program Text

Program Text (g01etce.c)

### 9.2  Program Data

Program Data (g01etce.d)

### 9.3  Program Results

Program Results (g01etce.r)