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T. Koshy (2018)
Fibonacci and Lucas Numbers With Applications
E. Tan, Semih Yilmaz, Murat Sahin (2016)
A note on bi-periodic Fibonacci and Lucas quaternionsChaos Solitons & Fractals, 85
E. Tan, Semih Yilmaz, Murat Sahin (2016)
On a new generalization of Fibonacci quaternionsChaos Solitons & Fractals, 82
H. Hime (1894)
“The Elements of Quaternions”Nature, 51
Yanwei Liu, Xia Liu, Shanshan Li, Ruiqi Wang, Zengrong Liu (2015)
The Bogdanov-Takens bifurcation study of 2m coupled neurons system with 2m+1$2m+1$ delaysAdvances in Difference Equations, 2015
Emrah Polatlı, Seyhun Kesim (2015)
On quaternions with generalized Fibonacci and Lucas number componentsAdvances in Difference Equations, 2015
M. Akyiğit, Hidayet Kösal, M. Tosun (2014)
Fibonacci Generalized QuaternionsAdvances in Applied Clifford Algebras, 24
S. Halici (2012)
On Fibonacci QuaternionsAdvances in Applied Clifford Algebras, 22
MR Iyer (1969)
A note on Fibonacci quaternionsThe Fibonacci Quarterly, 7
S. Halici (2016)
On a Generalization for Quaternion SequencesarXiv: Rings and Algebras
Merve Özvatan (2018)
Generalized Golden-Fibonacci calculus and applications
Emrah Polatlı (2016)
A Generalization of Fibonacci and Lucas QuaternionsAdvances in Applied Clifford Algebras, 26
A. Horadam (1963)
Complex Fibonacci Numbers and Fibonacci QuaternionsAmerican Mathematical Monthly, 70
S. Vajda (1989)
Fibonacci and Lucas Numbers and the Golden Section
C Kızılateş (2019)
On quaternions with incomplete Fibonacci and Lucas numbers componentsUtilitas Mathematica, 110
A. Hardy, A. Christie (2007)
ELEMENTS OF QUATERNIONS.Science, 2 75
T. Koshy (2001)
Fibonacci and Lucas Numbers with Applications: Koshy/Fibonacci
S. Halici, A. Karataş (2017)
On a generalization for fibonacci quaternionsChaos Solitons & Fractals, 98
(1993)
Quaternion recurrence relations
Emrah Polatlı (2018)
On Certain Properties of Quadrapell QuaternionsKaraelmas Science and Engineering Journal
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In this paper, with the help of higher order Fibonacci numbers, we introduce higher order Fibonacci quaternions that generalize the Fibonacci quaternions studied by Horadam and Halıcı. We give recurrence relation, Binet formula, generating and exponential generating functions and some other algebraic properties of higher order Fibonacci quaternions.
The Journal of Analysis – Springer Journals
Published: Dec 1, 2021
Keywords: Fibonacci quaternions; Higher order Fibonacci quaternions; Recurrence relation; Generating functions; 11B39; 11R52; 05A15
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