# NAG CL Interfaceg01qtc (pdf_​landau_​moment2)

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## 1Purpose

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

## 2Specification

 #include
 double g01qtc (double x)
The function may be called by the names: g01qtc, nag_stat_pdf_landau_moment2 or nag_moment_2_landau.

## 3Description

g01qtc evaluates an approximation to the second moment ${\Phi }_{2}\left(x\right)$ of the Landau density function given by
 $Φ2(x)=1Φ(x) ∫-∞xλ2ϕ(λ)dλ,$
where $\varphi \left(\lambda \right)$ is described in g01mtc, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of ${\Phi }_{1}\left(x\right)$, g01ptc can be used.

## 4References

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

## 5Arguments

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

None.

## 7Accuracy

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.

## 8Parallelism and Performance

g01qtc is not threaded in any implementation.

None.

## 10Example

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

### 10.1Program Text

Program Text (g01qtce.c)

### 10.2Program Data

Program Data (g01qtce.d)

### 10.3Program Results

Program Results (g01qtce.r)