<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>ih</italic> = <italic>−hi</italic> = <italic>ɛ</italic> + <italic>i</italic>. 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.</p></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.

The Hybrid Numbers of Padovan and Some Identities

University of Trás-os-Montes and Alto Douro

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"The Hybrid Numbers of Padovan and Some Identities"}

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...

The Hybrid Numbers of Padovan and Some Identities

Online veröffentlicht: 16. Juli 2020

Seitenbereich: 256 - 267

Eingereicht: 14. Okt. 2019

Akzeptiert: 28. Juni 2020

DOI: https://doi.org/10.2478/amsil-2020-0019

Schlüsselwörter
Binet’s formula, hybrid numbers, Padovan sequence, hybrid Padovan number

© 2020 Milena Carolina dos Santos Mangueira et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

The Hybrid Numbers of Padovan and Some Identities

Online veröffentlicht: 16. Juli 2020

Seitenbereich: 256 - 267

Eingereicht: 14. Okt. 2019

Akzeptiert: 28. Juni 2020

DOI: https://doi.org/10.2478/amsil-2020-0019

SchlüsselwörterBinet’s formula, hybrid numbers, Padovan sequence, hybrid Padovan number

© 2020 Milena Carolina dos Santos Mangueira et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Schlüsselwörter
Binet’s formula, hybrid numbers, Padovan sequence, hybrid Padovan number