NAG Library Function Document

1Purpose

nag_moment_1_landau (g01ptc) returns the value of the first moment ${\Phi }_{1}\left(x\right)$ of the Landau density function.

2Specification

 #include #include
 double nag_moment_1_landau (double x)

3Description

nag_moment_1_landau (g01ptc) 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 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 ${\Phi }_{2}\left(x\right)$, nag_moment_2_landau (g01qtc) 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 $x$ 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

nag_moment_1_landau (g01ptc) is not threaded in any implementation.

None.

10Example

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

10.1Program Text

Program Text (g01ptce.c)

10.2Program Data

Program Data (g01ptce.d)

10.3Program Results

Program Results (g01ptce.r)

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