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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_stat_pdf_landau_moment1 (g01pt)

## Purpose

nag_stat_pdf_landau_moment1 (g01pt) returns the value of the first moment ${\Phi }_{1}\left(x\right)$ of the Landau density function.

## Syntax

[result] = g01pt(x)
[result] = nag_stat_pdf_landau_moment1(x)

## Description

nag_stat_pdf_landau_moment1 (g01pt) evaluates an approximation to the first moment ${\Phi }_{1}\left(x\right)$ of the Landau density function given by
 $Φ1x=1Φx ∫-∞xλϕλdλ,$
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 ${\Phi }_{2}\left(x\right)$, nag_stat_pdf_landau_moment2 (g01qt) 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 $x$ 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.

None.

## Example

This example evaluates ${\Phi }_{1}\left(x\right)$ at $x=0.5$, and prints the results.
```function g01pt_example

fprintf('g01pt example results\n\n');

x = 0.5;
[phi1] = g01pt(x);

fprintf('Phi_1(%5.2f) = %8.4f\n', x, phi1);

```
```g01pt example results

Phi_1( 0.50) =  -0.6293
```