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Axioms 2018, 7(3), 62; https://doi.org/10.3390/axioms7030062

Umbral Methods and Harmonic Numbers

1
ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Rome, Italy
2
Department of Methods and Mathematic Models for Applied Sciences, University of Rome, La Sapienza, Via A. Scarpa, 14, 00161 Rome, Italy
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 4 June 2018 / Revised: 22 August 2018 / Accepted: 24 August 2018 / Published: 1 September 2018
(This article belongs to the Special Issue Mathematical Analysis and Applications)
Full-Text   |   PDF [243 KB, uploaded 1 September 2018]

Abstract

The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals. View Full-Text
Keywords: harmonic numbers 11K99; operators 44A99, 47B99; umbral methods 05A40; special functions 33C52, 33C65, 33C99, 33B10, 33B15; Hermite polynomials 33C45 harmonic numbers 11K99; operators 44A99, 47B99; umbral methods 05A40; special functions 33C52, 33C65, 33C99, 33B10, 33B15; Hermite polynomials 33C45
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Dattoli, G.; Germano, B.; Licciardi, S.; Martinelli, M.R. Umbral Methods and Harmonic Numbers. Axioms 2018, 7, 62.

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