# NAG Library Function Document

## 1Purpose

nag_prob_der_landau (g01rtc) returns the value of the derivative ${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function.

## 2Specification

 #include #include
 double nag_prob_der_landau (double x)

## 3Description

nag_prob_der_landau (g01rtc) evaluates an approximation to the derivative ${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function given by
 $ϕ′λ=dϕλ dλ ,$
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 $\varphi \left(\lambda \right)$, nag_prob_density_landau (g01mtc) 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:    $\mathbf{x}$doubleInput
On entry: the argument $\lambda$ 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.
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.

## 8Parallelism and Performance

nag_prob_der_landau (g01rtc) is not threaded in any implementation.

None.

## 10Example

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

### 10.1Program Text

Program Text (g01rtce.c)

### 10.2Program Data

Program Data (g01rtce.d)

### 10.3Program Results

Program Results (g01rtce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017