# NAG Library Routine Document

## 1Purpose

g01etf returns the value of the Landau distribution function $\Phi \left(\lambda \right)$, via the routine name.

## 2Specification

Fortran Interface
 Function g01etf ( x)
 Real (Kind=nag_wp) :: g01etf Real (Kind=nag_wp), Intent (In) :: x
#include nagmk26.h
 double g01etf_ (const double *x)

## 3Description

g01etf evaluates an approximation to the Landau distribution function $\Phi \left(\lambda \right)$ given by
 $Φλ=∫-∞λϕλdλ,$
where $\varphi \left(\lambda \right)$ is described in g01mtf, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).

## 4References

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

## 5Arguments

1:     $\mathbf{x}$ – Real (Kind=nag_wp)Input
On entry: the argument $\lambda$ of the function.

None.

## 7Accuracy

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.

## 8Parallelism and Performance

g01etf is not threaded in any implementation.

None.

## 10Example

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

### 10.1Program Text

Program Text (g01etfe.f90)

### 10.2Program Data

Program Data (g01etfe.d)

### 10.3Program Results

Program Results (g01etfe.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017