g01rt returns the value of the derivative ${\varphi}^{\prime}\left(\lambda \right)$ of the Landau density function.

# Syntax

C# |
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public static double g01rt( double x ) |

Visual Basic |
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Public Shared Function g01rt ( _ x As Double _ ) As Double |

Visual C++ |
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public: static double g01rt( double x ) |

F# |
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static member g01rt : x : float -> float |

#### Parameters

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

#### Return Value

g01rt returns the value of the derivative ${\varphi}^{\prime}\left(\lambda \right)$ of the Landau density function.

# Description

g01rt evaluates an approximation to the derivative ${\varphi}^{\prime}\left(\lambda \right)$ of the Landau density function given by

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).

$${\varphi}^{\prime}\left(\lambda \right)=\frac{d\varphi \left(\lambda \right)}{d\lambda}\text{,}$$ |

To obtain the value of $\varphi \left(\lambda \right)$, g01mt
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 ${\varphi}^{\prime}\left(\lambda \right)$,
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.

# Parallelism and Performance

None.

# Further Comments

None.

# Example

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

Example program (C#): g01rte.cs