# NAG Library Routine Document

## 1Purpose

g01qtf returns the value of the second moment ${\Phi }_{2}\left(x\right)$ of the Landau density function, via the routine name.

## 2Specification

Fortran Interface
 Function g01qtf ( x)
 Real (Kind=nag_wp) :: g01qtf Real (Kind=nag_wp), Intent (In) :: x
#include nagmk26.h
 double g01qtf_ (const double *x)

## 3Description

g01qtf evaluates an approximation to the second moment ${\Phi }_{2}\left(x\right)$ of the Landau density function given by
 $Φ2x=1Φx ∫-∞xλ2ϕλdλ,$
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 ${\Phi }_{1}\left(x\right)$, g01ptf can be used.

## 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 $x$ 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.

## 8Parallelism and Performance

g01qtf is not threaded in any implementation.

None.

## 10Example

This example evaluates ${\Phi }_{2}\left(x\right)$ at $x=0.5$, and prints the results.

### 10.1Program Text

Program Text (g01qtfe.f90)

### 10.2Program Data

Program Data (g01qtfe.d)

### 10.3Program Results

Program Results (g01qtfe.r)

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