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Mathematics > Number Theory

arXiv:1805.04489 (math)
[Submitted on 11 May 2018]

Title:Convolution identities for scale transformations of Appell polynomials

Authors:José A. Adell, Alberto Lekuona
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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.
Subjects: Number Theory (math.NT)
Cite as: arXiv:1805.04489 [math.NT]
  (or arXiv:1805.04489v1 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.04489

Submission history

From: Jose Adell A. [view email]
[v1] Fri, 11 May 2018 16:52:33 UTC (12 KB)
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