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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_stat_pdf_landau_deriv (g01rt)

## Purpose

nag_stat_pdf_landau_deriv (g01rt) returns the value of the derivative ${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function.

## Syntax

[result] = g01rt(x)
[result] = nag_stat_pdf_landau_deriv(x)

## Description

nag_stat_pdf_landau_deriv (g01rt) evaluates an approximation to the derivative ${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function given by
 $ϕ′λ=dϕλ dλ ,$
where $\varphi \left(\lambda \right)$ is described in nag_stat_pdf_landau (g01mt), using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of $\varphi \left(\lambda \right)$, nag_stat_pdf_landau (g01mt) can be used.

## References

Kölbig K S and Schorr B (1984) A program package for the Landau distribution Comp. Phys. Comm. 31 97–111

## Parameters

### Compulsory Input Parameters

1:     $\mathrm{x}$ – double scalar
The argument $\lambda$ of the function.

None.

### Output Parameters

1:     $\mathrm{result}$ – double scalar
The result of the function.

None.

## 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 ${\varphi }^{\prime }\left(\lambda \right)$, which is of the order of $\mathrm{exp}\left[-\mathrm{exp}\left(-\lambda \right)\right]$, underflow may occur on some machines when $\lambda$ is moderately large and negative.

None.

## Example

This example evaluates ${\varphi }^{\prime }\left(\lambda \right)$ at $\lambda =0.5$, and prints the results.
```function g01rt_example

fprintf('g01rt example results\n\n');

x = 0.5;
[phid] = g01rt(x);

fprintf('phi''(%5.2f) = %8.4f\n', x, phid);

```
```g01rt example results

phi'( 0.50) =  -0.0360
```