Next Article in Journal / Special Issue
Cohomology Theory of Nonassociative Algebras with Metagroup Relations
Previous Article in Journal
Generalized Hyers–Ulam Stability of the Additive Functional Equation
Previous Article in Special Issue
Unification Theories: New Results and Examples
Article Menu

Export Article

Open AccessArticle

Dual Numbers and Operational Umbral Methods

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
ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Rome, Italy
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;
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)
PDF [268 KB, uploaded 2 July 2019]


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).

Share & Cite This Article

MDPI and ACS Style

Behr, N.; Dattoli, G.; Lattanzi, A.; Licciardi, S. Dual Numbers and Operational Umbral Methods. Axioms 2019, 8, 77.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top