nag_moment_2_landau (g01qtc) (PDF version)

g01 Chapter Contents

g01 Chapter Introduction

NAG Library Manual

NAG Library Function Document

nag_moment_2_landau (g01qtc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

+− 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1 Purpose

nag_moment_2_landau (g01qtc) returns the value of the second moment

Φ_{2} (x)

of the Landau density function.

2 Specification

#include <nag.h>

#include <nagg01.h>

double

nag_moment_2_landau (double x)

3 Description

nag_moment_2_landau (g01qtc) evaluates an approximation to the second moment

Φ_{2} (x)

of the Landau density function given by

Φ_{2} (x) = \frac{1}{Φ (x)} \int_{- \infty}^{x} λ^{2} ϕ (λ) d λ,

where

ϕ (λ)

is described in nag_prob_density_landau (g01mtc), using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).

To obtain the value of

Φ_{1} (x)

, nag_moment_1_landau (g01ptc) 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 – doubleInput: 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

Not applicable.

9 Further Comments

None.

10 Example

This example evaluates

Φ_{2} (x)

at

x = 0.5

, and prints the results.

10.1 Program Text

Program Text (g01qtce.c)

10.2 Program Data

Program Data (g01qtce.d)

10.3 Program Results

Program Results (g01qtce.r)

nag_moment_2_landau (g01qtc) (PDF version)

g01 Chapter Contents

g01 Chapter Introduction

NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014