Results 1 to 10 of about 908 (146)
On Fibonacci quaternions [PDF]
Advances in Applied Clifford Algebras, 2011 In this paper, we investigate the Fibonacci and Lucas quaternions. We give the generating functions and Binet formulas for these quaternions.
Halıcı, Serpil
core +8 more sources
On Generalized Fibonacci Quaternions and Fibonacci-Narayana Quaternions [PDF]
Advances in Applied Clifford Algebras, 2013 In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions.Comment: Accepted in Adv. in Appl.
Flaut, Cristina, Shpakivskyi, Vitalii
core +5 more sources
On the Bicomplex $k$-Fibonacci Quaternions
Communications in Advanced Mathematical Sciences, 2019 In this paper, bicomplex $k$-Fibonacci quaternions are defined. Also, some algebraic properties of bicomplex $k$-Fibonacci quaternions are investigated.
Fügen Torunbalcı Aydın
doaj +5 more sources
On Quaternion Gaussian Bronze Fibonacci Numbers [PDF]
Annales Mathematicae Silesianae, 2022 In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defined and studied. Binet’s formula, generating function and certain properties and identities are provided.
Catarino Paula, Ricardo Sandra
doaj +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.
Fügen Torunbalcı Aydın
+8 more sources
New Properties and Identities for Fibonacci Finite Operator Quaternions [PDF]
Mathematics, 2022 In this paper, with the help of the finite operators and Fibonacci numbers, we define a new family of quaternions whose components are the Fibonacci finite operator numbers. We also provide some properties of these types of quaternions.
Nazlıhan Terzioğlu +2 more
doaj +2 more sources
Journal of Science and Arts, 2021 In this paper, we define and study another interesting generalization of the Fibonacci quaternions is called k-order Fibonacci quaternions. Then we obtain for Fibonacci quaternions, for Tribonacci quaternions and for Tetranacci quaternions. We give generating function, the summation formula and some properties about k-order Fibonacci quaternions. Also,
Mustafa Aşçı, Süleyman Aydınyüz
openalex +4 more sources
Gelin-Cesáro identities for Fibonacci and Lucas quaternions [PDF]
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2019 To date, many identities of different quaternions, including the Fibonacci and Lucas quaternions, have been investigated. In this study, we present Gelin-Cesáro identities for Fibonacci and Lucas quaternions.
Ahmet Daşdemir
doaj +2 more sources
New summation identities of hyperbolic k-Fibonacci and k-Lucas quaternions [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we introduce a set of identities involving hyperbolic k-Fibonacci quaternions and k-Lucas quaternions. Moreover, we derive summation identities for hyperbolic k-Fibonacci and k-Lucas quaternions by utilizing established properties of k ...
A. D. Godase
doaj +2 more sources
Dual Fibonacci Quaternions [PDF]
Advances in Applied Clifford Algebras, 2013 In this study, we define the dual Fibonacci quaternion and the dual Lucas quternion. We derive the relations between the dual Fibonacci and the dual Lucas quaternion which connected the Fibonacci and the Lucas numbers. Furthermore, we give the Binet and Cassini formulas for these quaternions.
Semra Kaya Nurkan, İlkay Arslan Güven
openalex +6 more sources