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

# Syntax

C#
```public static double g01pt(
double x
)```
Visual Basic
```Public Shared Function g01pt ( _
x As Double _
) As Double```
Visual C++
```public:
static double g01pt(
double x
)```
F#
```static member g01pt :
x : float -> float
```

#### Parameters

x
Type: System..::..Double
On entry: the argument $x$ of the function.

#### Return Value

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

# Description

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 g01mt, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of ${\Phi }_{2}\left(x\right)$, 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

# Error Indicators and Warnings

There are no failure exits from this routine.

# 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.

None.

# Example

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

Example program (C#): g01pte.cs

Example program data: g01pte.d

Example program results: g01pte.r