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 (λ)

, nag_prob_density_landau (g01mtc) 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

nag_prob_der_landau (g01rtc) is not threaded in any implementation.

9

Further Comments

None.

10

Example

This example evaluates

ϕ^{'} (λ)

λ = 0.5

, and prints the results.

NAG Library Function Document

nag_prob_der_landau (g01rtc)

▸▿ 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

2

Specification

3

Description