


The Landau Distribution
=======================

.. function:: gsl_ran_landau()

 This function returns a random variate from the :index:`Landau
 distribution`. The probability distribution for Landau random
 variates is defined analytically by the complex integral,

 .. math::
   p(x) = (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,

 .. math::
   p(x) = (1/\pi) \int_0^\infty \exp(-t \log(t) - x t) \sin(\pi t) dt.

.. function:: gsl_ran_landau_pdf(x)

 This function computes the probability density :math:`p(x)` at :math:`x` for the
 Landau distribution using an approximation to the formula given above.
