G01 Chapter Contents
G01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentG01PTF

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

G01PTF returns the value of the first moment ${\Phi }_{1}\left(x\right)$ of the Landau density function, via the routine name.

## 2  Specification

 FUNCTION G01PTF ( X)
 REAL (KIND=nag_wp) G01PTF
 REAL (KIND=nag_wp) X

## 3  Description

G01PTF evaluates an approximation to the first moment ${\Phi }_{1}\left(x\right)$ of the Landau density function given by
 $Φ1x=1Φx ∫-∞xλϕλdλ,$
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).
To obtain the value of ${\Phi }_{2}\left(x\right)$, G01QTF can be used.

## 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 $x$ 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.

None.

## 9  Example

This example evaluates ${\Phi }_{1}\left(x\right)$ at $x=0.5$, and prints the results.

### 9.1  Program Text

Program Text (g01ptfe.f90)

### 9.2  Program Data

Program Data (g01ptfe.d)

### 9.3  Program Results

Program Results (g01ptfe.r)