On certain bihypernomials related to Pell and Pell-Lucas numbers

Year 2022, Volume: 71 Issue: 2, 422 - 433, 30.06.2022

Anetta Szynal-lıana , İwona Wloch , Mirosław Liana

https://doi.org/10.31801/cfsuasmas.890932

Cited By: 2

Abstract

The bihyperbolic numbers are extension of hyperbolic numbers to four dimensions. In this paper we introduce the concept of Pell and Pell-Lucas bihypernomials as a generalization of bihyperbolic Pell and Pell-Lucas numbers, respectively.

Keywords

Pell numbers, recurrence relations, hyperbolic numbers, bihyperbolic numbers, polynomials

References

• Bilgin, M., Ersoy, S., Algebraic properties of bihyperbolic numbers, Adv. Appl. Clifford Algebr., 30(13) (2020). https://doi.org/10.1007/s00006-019-1036-2
• Brod, D., Szynal-Liana, A., Wloch, I., Bihyperbolic numbers of the Fibonacci type and their idempotent representation, Comment. Math. Univ. Carolin., 62(4) (2021), 409-416. http://dx.doi.org/10.14712/1213-7243.2021.033
• Brod, D., Szynal-Liana, A., Wloch, I., On some combinatorial properties of bihyperbolic numbers of the Fibonacci type, Math. Methods Appl. Sci., 44(6) (2021), 4607-4615. https://doi.org/10.1002/mma.7054
• Halici, S., On the Pell polynomials, Appl. Math. Sci. (Ruse), 5(37) (2011), 1833–1838.
• Horadam, A. F., Minmax Sequences for Pell Numbers, In: Bergum G.E., Philippou A.N., Horadam A.F. (eds) Applications of Fibonacci Numbers, Springer, Dordrecht, 1996.
• Horadam, A. F., Pell identities, Fibonacci Quart., 9(3) (1971), 245–263.
• Horadam, A. F., Mahon, Bro J. M., Pell and Pell-Lucas polynomials, Fibonacci Quart., 23(1) (1985), 7–20.
• Horzum, T., Kocer, E. G., On some properties of Horadam polynomials, Int. Math. Forum, 25(4) (2009), 1243–1252.
• Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
• Rochon, D., Shapiro, M., On algebraic properties of bicomplex and hyperbolic numbers, An. Univ. Oradea Fasc. Mat., 11 (2004), 71–110.
• Sobczyk, G., The hyperbolic number plane, College Math. J., 26(4) (1995). https://doi.org/10.1080/07468342.1995.11973712
• Szynal-Liana, A., Wloch, I., On Pell and Pell-Lucas hybrid numbers, Comment. Math. Prace Mat., 58(1-2) (2018), 11–17. https://doi.org/10.14708/cm.v58i1-2.6364
• Szynal-Liana, A., Wloch, I., The Pell quaternions and the Pell octonions, Adv. Appl. Clifford Algebr., 26 (2016), 435–440. https://doi.org/10.1007/s00006-015-0570-9
• Szynal-Liana, A., Wloch, I., Hypercomplex Numbers of the Fibonacci Type, Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszow, 2019.