Geodesic
Algebraic Properties of Bi-periodic Dual Fibonacci Quaternions
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 1, p. 99 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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The purpose of the paper is to construct a new representation of dual quaternions called bi-periodic dual Fibonacci quaternions. These quaternions are originated as a generalization of the known quaternions in literature such as dual Fibonacci quaternions, dual Pell quaternions and dual $k$-Fibonacci quaternions. Moreover, some of them have not been introduced until now. Finally, we calculate the generating function, Binet formula and Catalan's identity of the bi-periodic dual Fibonacci quaternions.
Classification : 11B39 05A15, 11R52
Keywords: Dual Fibonacci quaternions, bi-periodic Fibonacci quaternions, bi-periodic dual Fibonacci quaternions 
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     author = {F. Ate\c{s} and I. G\"ok and N. Ekmekci},
     title = {Algebraic {Properties} of {Bi-periodic} {Dual} {Fibonacci} {Quaternions}},
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F. Ateş; I. Gök; N. Ekmekci. Algebraic Properties of Bi-periodic Dual Fibonacci Quaternions. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 1, p. 99 . http://geodesic.mathdoc.fr/item/KJM_2019_43_1_a8/