g01mt returns the value of the Landau density function $\varphi \left(\lambda \right)$.

# Syntax

C#
```public static double g01mt(
double x
)```
Visual Basic
```Public Shared Function g01mt ( _
x As Double _
) As Double```
Visual C++
```public:
static double g01mt(
double x
)```
F#
```static member g01mt :
x : float -> float
```

#### Parameters

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

#### Return Value

g01mt returns the value of the Landau density function $\varphi \left(\lambda \right)$.

# Description

g01mt evaluates an approximation to the Landau density function $\varphi \left(\lambda \right)$ given by
 $ϕλ=12πi∫c-i∞c+i∞expλs+sln sds,$
where $c$ is an arbitrary real constant, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of ${\varphi }^{\prime }\left(\lambda \right)$, g01rt 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.
Because of the asymptotic behaviour of $\varphi \left(\lambda \right)$, 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.

None.

# Example

This example evaluates $\varphi \left(\lambda \right)$ at $\lambda =0.5$, and prints the results.

Example program (C#): g01mte.cs

Example program data: g01mte.d

Example program results: g01mte.r