G01 Chapter Contents
G01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentG01ETF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

G01ETF returns the value of the Landau distribution function $\Phi \left(\lambda \right)$, via the routine name.

## 2  Specification

 FUNCTION G01ETF ( X)
 REAL (KIND=nag_wp) G01ETF
 REAL (KIND=nag_wp) X

## 3  Description

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).

## 4  References

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

## 5  Parameters

1:     X – REAL (KIND=nag_wp)Input
On entry: the argument $\lambda$ of the function.

## 6  Error Indicators and Warnings

There are no failure exits from this routine.

## 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 (g01etfe.f90)

### 9.2  Program Data

Program Data (g01etfe.d)

### 9.3  Program Results

Program Results (g01etfe.r)