Results 21 to 30 of about 185 (126)

On a new generalization of Fibonacci quaternions

Chaos, Solitons & Fractals, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tan, Elif, Yilmaz, Semih, Sahina, Murat
openaire   +3 more sources

Copper ratio obtained by generalizing the Fibonacci sequence

AIP Advances
In this study, we define a new generalization of the Fibonacci sequence that gives the copper ratio, and we will call it the copper Fibonacci sequence. In addition, inspired by the copper Fibonacci definition, we also define copper Lucas sequences, and ...
Engin Özkan, Hakan Akkuş
doaj   +3 more sources

A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In order to investigate the relationship between Gaussian Fibonacci numbers and quantum numbers and to develop both a deeper theoretical understanding in this study, q-Gaussian Fibonacci, q-Gaussian Lucas quaternions and polynomials are taken with ...
Bahar Kuloğlu
doaj   +2 more sources

On Bicomplex (p,q)-Fibonacci Quaternions

Mathematics
Here, we describe the bicomplex p,q-Fibonacci numbers and the bicomplex p,q-Fibonacci quaternions based on these numbers to show that bicomplex numbers are not defined the same as bicomplex quaternions.
Çağla Çelemoğlu
doaj   +2 more sources

Properties of Generalized Bronze Fibonacci Sequences and Their Hyperbolic Quaternions

Axioms
In this study, we establish some properties of Bronze Fibonacci and Bronze Lucas sequences. Then we find the relationships between the roots of the characteristic equation of these sequences with these sequences.
Engin Özkan, Hakan Akkuş, Alkan Özkan
doaj   +2 more sources

On Generalized Fibonacci Quaternions and Fibonacci-Narayana Quaternions [PDF]

Advances in Applied Clifford Algebras, 2013
Accepted in Adv. in Appl.
Flaut, Cristina, Shpakivskyi, Vitalii
openaire   +3 more sources

Pauli–Fibonacci quaternions [PDF]

Notes on Number Theory and Discrete Mathematics, 2021
The aim of this work is to consider the Pauli–Fibonacci quaternions and to present some properties involving this sequence, including the Binet’s formula and generating functions. Furthermore, the Honsberger identity, the generating function, d’Ocagne’s identity, Cassini’s identity, Catalan’s identity for these quaternions are given.
  +7 more sources

Construction of dual-generalized complex Fibonacci and Lucas quaternions

Karpatsʹkì Matematičnì Publìkacìï, 2022
The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formulas, Tagiuri's (
G.Y. Şentürk, N. Gürses, S. Yüce
doaj   +1 more source

SOME PROPERTIES OF BIVARIATE FIBONACCI AND LUCAS QUATERNION POLYNOMIALS [PDF]

, 2020
In this work, we introduce bivariate Fibonacci quaternion polynomials andbivariate Lucas quaternion polynomials. We present generating function,Binet formula, matrix representation, binomial formulas and some basicidentities for the bivariate Fibonacci ...
Ozturk, Arzu Ozkoc, Özkoç Öztürk, Arzu, Kaplan, Faruk   +2 more
core   +1 more source

On a Generalization of Incomplete Fibonacci Quaternions

The Journal of the Indian Mathematical Society, 2021
The aim of this article is to introduce a new class of quater- nions, namely, incomplete Horadam quaternions that are based on in- complete Horadam numbers which generalize the previously introduced incomplete Fibonacci and Lucas quaternions. Further, some identities including summation formulas and generating functions concerning these quaternions are
Bijan Kumar Patel, Narmada Behera
openaire   +2 more sources