Convolution identities for scale transformations of Appell polynomials
Number Theory
2018-05-14 v1
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.
Cite
@article{arxiv.1805.04489,
title = {Convolution identities for scale transformations of Appell polynomials},
author = {José A. Adell and Alberto Lekuona},
journal= {arXiv preprint arXiv:1805.04489},
year = {2018}
}