Landau distribution

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In probability theory, a branch of mathematics, the Landau distribution is a probability distribution defined by the complex integral

$p(x) = \frac{1}{2 \pi i} \int_{c-i\infty}^{c+i\infty}\! \exp(s \log s + x s)\, ds.$

For numerical purposes it is more convenient to use the following equivalent form of the integral,

$p(x) = \frac{1}{\pi} \int_0^\infty\! \exp(-t \log t - x t) \sin(\pi t)\, dt.$

The Landau distribution is used in physics to describe the fluctuations in the energy loss of a charged particle passing through a thin layer of matter.

From GSL manual, used under GFDL.

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Landau distribution

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