The probability generating function is a powerful technique for studying the law of finite sums of independent discrete random variables taking integer positive values. For real valued discrete random variables, the well known elementary theory of Dirichlet series and the symbolic computation packages available nowadays, such as Mathematica 5 TM, allows us to extend to general discrete random variables this technique. Being so, the purpose of this work is twofold. Firstly we show that discrete

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... andom variables taking real values, non necessarily integer or rational, may be studied with probability generating functions. Secondly we intend to draw attention to some practical ways of performing the necessary calculations.