On a new generalization of Fibonacci hybrid numbers

The hybrid numbers were introduced by Ozdemir [9] as a new generalization of complex, dual, and hyperbolic numbers. A hybrid number is defined by \(k=a+bi+c\epsilon +dh\), where \(a,b,c,d\) are real numbers and \(% i,\epsilon ,h\) are operators such that \(i^{2}=-1,\epsilon ^{2}=0,h^{2}=1\) and \(ih...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Tan, Elif, N Rosa Ait-Amrane
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.06.2020
Subjects
Fibonacci numbers
Operators (mathematics)
Real numbers
Online AccessGet full text

Cover

More Information
Summary:The hybrid numbers were introduced by Ozdemir [9] as a new generalization of complex, dual, and hyperbolic numbers. A hybrid number is defined by \(k=a+bi+c\epsilon +dh\), where \(a,b,c,d\) are real numbers and \(% i,\epsilon ,h\) are operators such that \(i^{2}=-1,\epsilon ^{2}=0,h^{2}=1\) and \(ih=-hi=\epsilon +i\). This work is intended as an attempt to introduce the bi-periodic Horadam hybrid numbers which generalize the classical Horadam hybrid numbers. We give the generating function, the Binet formula, and some basic properties of these new hybrid numbers. Also, we investigate some relationships between generalized bi-periodic Fibonacci hybrid numbers and generalized bi-periodic\ Lucas hybrid numbers.
ISSN:2331-8422