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Dual Numbers and Operational Umbral Methods

1
Institut de Recherche en Informatique Fondamentale (IRIF), Université de Paris, Bâtiment Sophie Germain, Case Courier 7014, 8 Place Aurélie Nemours, CEDEX 13, 75205 Paris, France
2
ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Rome, Italy
3
H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Science, ul. Radzikowskiego 152, 31-342 Kraków, Poland
*
Author to whom correspondence should be addressed.
Axioms 2019, 8(3), 77; https://doi.org/10.3390/axioms8030077
Received: 22 May 2019 / Revised: 25 June 2019 / Accepted: 26 June 2019 / Published: 2 July 2019
(This article belongs to the Special Issue Non-associative Structures and Other Related Structures)
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PDF [268 KB, uploaded 2 July 2019]

Abstract

Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus. Based on the relevant algebraic rules and matrix realizations of dual numbers, we present a novel point of view, embedding dual numbers within a formalism reminiscent of operational umbral calculus. View Full-Text
Keywords: dual numbers; operational methods; umbral image techniques dual numbers; operational methods; umbral image techniques
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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Behr, N.; Dattoli, G.; Lattanzi, A.; Licciardi, S. Dual Numbers and Operational Umbral Methods. Axioms 2019, 8, 77.

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