Explicit expressions for a certain subset of Appell polynomials: a probabilistic perspective. (English) Zbl 1476.11036
Summary: We consider the subset \(\mathcal E\) of Appell polynomials whose generating function is given in terms of a real power of the moment generating function of a certain random variable \(Y\). This subset contains different kinds of generalizations of the Bernoulli, Apostol-Euler, Cauchy-type, Hermite, and Miller-Lee polynomials, among others. We give a unified approach to obtain explicit expressions for those Appell sequences in \(\mathcal{E}\). The main tool is a suitable probabilistic generalization of the Stirling numbers of the second kind.
MSC:
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 11B73 | Bell and Stirling numbers |
| 60E05 | Probability distributions: general theory |
| 60E10 | Characteristic functions; other transforms |
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