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- Function:
*double***gsl_ran_levy***(const gsl_rng **`r`, double`c`, double`alpha`) -
This function returns a random variate from the Levy symmetric stable distribution with scale

`c`and exponent`alpha`. The symmetric stable probability distribution is defined by a Fourier transform,p(x) = {1 \over 2 \pi} \int_{-\infty}^{+\infty} dt \exp(-it x - |c t|^alpha)

There is no explicit solution for the form of

*p(x)*and the library does not define a corresponding`pdf`

function. For*\alpha = 1*the distribution reduces to the Cauchy distribution. For*\alpha = 2*it is a Gaussian distribution with*\sigma = \sqrt{2} c*. For*\alpha < 1*the tails of the distribution become extremely wide.The algorithm only works for

*0 < alpha <= 2*.