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.

Umbral nature of the Poisson random variables

DI NARDO, Elvira;
2001-01-01

Abstract

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.
2001
Algebraic Combinatorics and Computer Science: a tribute to Gian-Carlo Rota
Springer-Verlag
unico
245
266
9788847000780
http://arxiv.org/abs/math/0412054
moment symbolic method; Poisson random variables
DI NARDO E.; D. SENATO PULLANO
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1561362
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