Umbral nature of the Poisson random variables

Details Umbral nature of the Poisson random variables Umbral nature of the Poisson random variables

2004-12-02

arxiv.org/abs/math/0412054v1

Mathematics

Probability

23 pages

Scientific paper

Extending the rigorous presentation of the classical umbral calculus given by Rota and Taylor in 1994, the so-called partition polynomials are interpreted with the aim to point out the umbral nature of the Poisson random variables. Among the new umbrae introduced, the main tool is the partition umbra that leads also to a simple expression of the functional composition of the exponential power series. Moreover a new short proof of the Lagrange inversion formula is given.

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