NAG Library Routine Document

g01qtf (pdf_landau_moment2)

1
Purpose

g01qtf returns the value of the second moment Φ2x of the Landau density function.

2
Specification

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

3
Description

g01qtf evaluates an approximation to the second moment Φ2 x of the Landau density function given by
Φ2x=1Φx -xλ2ϕλdλ,  
where ϕλ 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 Φ1x, g01ptf 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
Arguments

1:     x – Real (Kind=nag_wp)Input
On entry: the argument x of the function.

6
Error Indicators and Warnings

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.

8
Parallelism and Performance

g01qtf is not threaded in any implementation.

9
Further Comments

None.

10
Example

This example evaluates Φ2x at x=0.5, and prints the results.

10.1
Program Text

Program Text (g01qtfe.f90)

10.2
Program Data

Program Data (g01qtfe.d)

10.3
Program Results

Program Results (g01qtfe.r)