NAG Library Function Document

nag_prob_density_landau (g01mtc)

+− 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_prob_density_landau (g01mtc) returns the value of the Landau density function

ϕ (λ)

2 Specification

#include <nag.h>

#include <nagg01.h>

double

nag_prob_density_landau (double x)

3 Description

nag_prob_density_landau (g01mtc) evaluates an approximation to the Landau density function

ϕ (λ)

given by

ϕ (λ) = \frac{1}{2 π i} \int_{c - i \infty}^{c + i \infty} \exp (λ s + s \ln s) d s,

where

c

is an arbitrary real constant, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).

To obtain the value of

ϕ^{'} (λ)

, nag_prob_der_landau (g01rtc) 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 $λ$ 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.

Because of the asymptotic behaviour of

ϕ (λ)

, which is of the order of

\exp [- \exp (- λ)]

, underflow may occur on some machines when

λ

is moderately large and negative.

8 Parallelism and Performance

Not applicable.

9 Further Comments

None.

10 Example

This example evaluates

ϕ (λ)

λ = 0.5

, and prints the results.

NAG Library Function Documentnag_prob_density_landau (g01mtc)