Some remarks regarding the $(p,q)-$Fibonacci and Lucas octonion polynomials

Year 2018, , 46 - 53, 11.03.2018

Arzu Özkoç Öztürk , Ayhan Porsuk

https://doi.org/10.32323/ujma.386520

Cited By: 3

Abstract

We investigate the $(p,q)-$Fibonacci and Lucas octonion polynomials. The main purpose of this paper is using of some properties of the $(p,q)-$ Fibonacci and Lucas polynomials. Also for present some results involving these octonion polynomials, we obtain some interesting computational formulas.

Keywords

Fibonacci Polynomials, Generating Functions, Fibonacci Octonions

References

• [1] M. Akyiğit, H. Kösal, M Tosun, Fibonacci Generalized Quaternions. Adv. Appl. Clifford Algebr. 24(3)(2014), 631–641.
• [2] A. İpek, K. Arı, On $h(x)-$Fibonacci Octonion Polynomials, Alabama Journal of Mathematics, 39, 2015.
• [3] A. İpek, C. Çimen, On $(p,q)-$Fibonacci Octonions. Mathematica Æterna, 6(6)(2016), 923-932.
• [4] O. Keçilioğlu, İ. Akkuş¸, The Fibonacci Octonions, Adv. App Clifford Algebras 25(2015) 151-158.
• [5] G. Y. Lee and M. Asci, Some Properties of the $(p,q)-$ Fibonacci and $(p,q)-$Lucas Polynomials, Journal of Applied Mathematics, Volume 2012, Article ID 264842, 18 pages doi:10.1155/2012/264842.
• [6] A .Nalli, P. Haukkanen, On generalized Fibonacci and Lucas Polynomials, Chaos Solitons and Fractals 42(2009) 3179-3186.
• [7] A. Özkoç¸, A. Porsuk, A Note for the $(p,q)-$Fibonacci and Lucas Quaternions Polynomials. Konuralp Journal of Mathematics. 5(2)(2017), 36-46.
• [8] P. Ribenboim, My Numbers, My Friends, Popular Lectures on Number Theory, Springer-Verlag, New York, Inc. 2000.
• [9] A Tekcan, A. Özkoc¸, M. Engür, M.E. Özbek, On Algebraic Identities on a New Integer Sequence with Four Parameters, Ars Combinatoria. 127(2016) 225-238.
• [10] J. Wang, Some New Results for the (p;q)􀀀 Fibonacci and Lucas Polynomials. Advances in Difference Equations 2014, 2014: 64.