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The Hybrid Numbers of Padovan and Some Identities Cover

Abstract

In this article, we will define Padovan’s hybrid numbers, based on the new noncommutative numbering system studied by Özdemir ([7]). Such a system that is a set involving complex, hyperbolic and dual numbers. In addition, Padovan’s hybrid numbers are created by combining this set, satisfying the relation ih = −hi = ɛ + i. Given this, some properties and identities are shown for these numbers, such as Binet’s formula, generating matrix, characteristic equation, norm, and generating function. In addition, these numbers are extended to the integer field and some identities are made.

DOI: https://doi.org/10.2478/amsil-2020-0019 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107
Language: English
Page range: 256 - 267
Submitted on: Oct 14, 2019
Accepted on: Jun 28, 2020
Published on: Jul 16, 2020
Published by: University of Silesia in Katowice, Institute of Mathematics
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2020 Milena Carolina dos Santos Mangueira, Renata Passos Machado Vieira, Francisco Régis Vieira Alves, Paula Maria Machado Cruz Catarino, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.