Hyper-Fibonacci and Hyper-Lucas Polynomials

Year 2023, , 63 - 70, 30.06.2023

Efruz Özlem Mersin

https://doi.org/10.47000/tjmcs.1123369

Cited By: 1

Abstract

In this paper, hyper-Fibonacci and hyper-Lucas polynomials are defined and some of their algebraic and combinatorial properties such as the recurrence relations, summation formulas, and generating functions are presented. In addition, some relationships between the hyper-Fibonacci and hyper-Lucas polynomials are given.

Keywords

Hyper-Fibonacci numbers, hyper-Lucas numbers, polynomials

References

• Bahşi, M., Mezö, I., Solak S., A symmetric algorithm for hyper-Fibonacci and hyper-Lucas numbers, Annales Mathematicae et Informaticae, 43(2014), 19–27.
• Bicknell, M., A primer for the Fibonacci numbers VII, The Fibonacci Quarterly, 8(4)(1970), 407–420.
• Bicknell, M., Hoggatt, Jr.V.E., Roots of Fibonacci Polynomials, The Fibonacci Quarterly, 11(5)(1973), 271–274.
• Catarino, P., A note on h (x)- Fibonacci quaternion polynomials, Chaos, Solitons and Fractals, 77(2015), 1–5.
• Catarino, P., The h (x)- Fibonacci quaternion polynomials: some combinatorial properties, Advances in Applied Clifford Algebras, 26(2016), 71–79.
• Dil, A., Mezö, I., A symmetric algorithm hyperharmonic and Fibonacci numbers, Applied Mathematics and Computation, 206(2008), 942–951.
• Dumont, D., Euler-Seidel matrices (Matrices d’Euler-Seidel), S´eminaire Lotharingien de Combinatoire [electronic only], (1981), B05c-25.
• Graham, R.L., Knuth, D.E., Patashnik, O., Concrete Mathematics, Addison Wesley, Reading, MA., 1993.
• Horzum, T., Koçer, E.G., On some properties of Horadam polynomials, International Mathematical Forum, 4(25) (2009), 1243–1252.
• Kilic, E., Tasci, D., Negatively subscripted Fibonacci and Lucas numbers and their complex factorizations, Ars Combinatoria, 96(2010), 275–288.
• Kızılateş, C., A note on Horadam hybrinomials, Fundamental Journal of Mathematics and Applications, 5(1)(2022), 1–9.
• Koshy, T., Fibonacci and Lucas Numbers with Applications, Pure and Applied Mathematics, A Wiley-Interscience Series of Texts, Monographs, and Tracts, New York: Wiley, 2001.
• Özdemir, G., Şimşek, Y., Generating functions for two variable polynomials related to a family of Fibonacci type polynomials and numbers, Filomat, 30(4)(2016), 969–975.
• Özkan, E., Altun, İ., Generalized Lucas polynomials and relationships between the Fibonacci polynomials and Lucas polynomials, Communications in Algebra, 47(10)(2019), 4020–4030.
• Soykan, Y., On generalized Fibonacci polynomials: Horadam polynomials, Earthline Journal of Mathematical Sciences, 11(1)(2023), 23–114.
• Szynal-Liana, A., Wloch, I., Generalized Fibonacci-Pell hybrinomials, Online Journal of Analytic Combinatorics, 15(2020), 1–12.
• Szynal-Liana, A.,Wloch, I., Introduction to Fibonacci and Lucas hybrinomials, Complex Variables and Elliptic Equations, 65(10)(2020), 1736–1747.
• Webb, W.A., Parberry, E.A., Divisibility properties of Fibonacci polynomials, The Fibonacci Quarterly, 7(5)(1969), 457–463.
• Yuan, Y., Zhang, W., Some identities involving the Fibonacci polynomials, The Fibonacci Quarterly, 40(4)(2002), 314–318.