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arXiv · 1711.02603

Explicit expressions for a certain class of Appell polynomials. A probabilistic approach

José A. Adell·Alberto Lekuona
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Abstract

We consider the class $\mathcal{E}_t(Y)$ of Appell polynomials whose generating function is given by means of a real power $t$ of the moment generating function of a certain random variable $Y$. For such polynomials, we obtain explicit expressions depending on the moments of $Y$. It turns out that various kinds of generalizations of Bernoulli and Apostol-Euler polynomials belong to $\mathcal{E}_t(Y)$ and can be written and investigated in a unified way. In particular, explicit expression for such polynomials can be given in terms of suitable probabilistic generalizations of the Stirling numbers of the second kind.

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José A. Adell, Alberto Lekuona. 2017-11-07. Explicit expressions for a certain class of Appell polynomials. A probabilistic approach. https://arxiv.org/abs/1711.02603

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