Results 21 to 30 of about 228 (120)
AxiomsIn this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions.
Can Kızılateş +3 more
doaj +2 more sources
Some Matrix Representations of Fibonacci Quaternions and Octonions
Advances in Applied Clifford Algebras, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Halıcı, Serpil, Karataş, Adnan
openaire +7 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
On a generalization of dual-generalized complex Fibonacci quaternions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this study, we introduce a new class of generalized quaternions whose components are dual-generalized complex Horadam numbers. We investigate some algebraic properties of them.
Elif Tan, Umut Öcal
doaj +1 more source
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
On Fibonacci quaternion matrix [PDF]
Notes on Number Theory and Discrete Mathematics, 2021 In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini’s identity using this new matrix.
Serpil Halici, Ömür Deveci
openaire +3 more sources
On Quaternion-Gaussian Fibonacci Numbers and Their Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients.
Halici Serpil, Cerda-Morales Gamaliel
doaj +1 more source
Hybrid Quaternions of Leonardo
Trends in Computational and Applied Mathematics, 2022 In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo, quaternions and hybrid numbers were presented.
M. C. S. Mangueira +2 more
doaj +1 more source
Quaternion Algebras and Generalized Fibonacci–Lucas Quaternions [PDF]
Advances in Applied Clifford Algebras, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Flaut, Cristina, Savin, Diana
openaire +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