On the Laplace transform of the Fr{e}chet distribution

We calculate exactly the Laplace transform of the Fr{e}chet distribution in the form $gamma x^{-(1+gamma)} exp(-x^{-gamma})$, $gamma > 0$, $0 leq x < infty$, for arbitrary rational values of the shape parameter $gamma$, i.e. for $gamma = l/k$ with $l, k = 1,2, ldots$. The method employs the inverse Mellin transform. The closed form expressions are obtained in terms of Meijer G functions and their graphical illustrations are provided. A rescaled Fr{e}chet distribution serves as a kernel of Fr{e}chet integral transform. It turns out that the Fr{e}chet transform of one-sided L{e}vy law reproduces the Fr{e}chet distribution.