nag_moment_2_landau (g01qtc) (PDF version)
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NAG Library Manual

# NAG Library Function Documentnag_moment_2_landau (g01qtc)

## 1  Purpose

nag_moment_2_landau (g01qtc) returns the value of the second moment ${\Phi }_{2}\left(x\right)$ of the Landau density function.

## 2  Specification

 #include #include
 double nag_moment_2_landau (double x)

## 3  Description

nag_moment_2_landau (g01qtc) evaluates an approximation to the second moment ${\Phi }_{2}\left(x\right)$ of the Landau density function given by
 $Φ2x=1Φx ∫-∞xλ2ϕλdλ,$
where $\varphi \left(\lambda \right)$ 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 ${\Phi }_{1}\left(x\right)$, nag_moment_1_landau (g01ptc) can be used.
Kölbig K S and Schorr B (1984) A program package for the Landau distribution Comp. Phys. Comm. 31 97–111

## 5  Arguments

1:    $\mathbf{x}$doubleInput
On entry: the argument $x$ of the function.

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.

Not applicable.

None.

## 10  Example

This example evaluates ${\Phi }_{2}\left(x\right)$ at $x=0.5$, and prints the results.

### 10.1  Program Text

Program Text (g01qtce.c)

### 10.2  Program Data

Program Data (g01qtce.d)

### 10.3  Program Results

Program Results (g01qtce.r)

nag_moment_2_landau (g01qtc) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG Library Manual