The distribution of sums of i.i.d. Pareto random variables with arbitrary shape parameter

Laplace transforms are used to derive an exact expression for the cdf of the sum of n i.i.d. Pareto random variables with common pdf f(x)=(alpha/beta)(1 + x/beta)(-alpha-1) for x > 0, where alpha > 0 and is not an integer, and beta > 0. An attractive feature of this expression is that it involves an integral of non oscillating real-valued functions on the positive real line. Examples of values of cdfs are provided and are compared to those determined via simulations.