Convolution identities for scale transformations of Appell polynomials

2018/05/11 by Adell, José A., Lekuona, Alberto
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1805.04489

Abstract

We obtain closed form expressions for convolutions of scale transformations within a certain subset of Appell polynomials. This subset contains the Bernoulli, Apostol-Euler, and Cauchy polynomials, as well as various kinds of their generalizations, among others. We give a unified approach mainly based on a probabilistic generalization of the Stirling numbers of the second kind. Different illustrative examples, including reformulations of convolution identities already known in the literature, are discussed in detail.

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