NAG Library Routine Document

G01MTF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

+− 9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1 Purpose

G01MTF returns the value of the Landau density function

ϕ (λ)

, via the routine name.

2 Specification

FUNCTION G01MTF (

REAL (KIND=nag_wp) G01MTF

REAL (KIND=nag_wp)

3 Description

G01MTF 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)

, G01RTF 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 $λ$ 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.

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 Further Comments

None.

9 Example

This example evaluates

ϕ (λ)

λ = 0.5

, and prints the results.

NAG Library Routine DocumentG01MTF