On Some k-Oresme Polynomials with Negative Indices

Year 2024, Volume: 7 Issue: 2, 71 - 79, 30.06.2024

Elifcan Sayın , Serpil Halıcı

https://doi.org/10.33434/cams.1444712

Abstract

In this study, \textit{k-} Oresme polynomials with negative indices, which are the generalization of Oresme polynomials, were examined and defined. By examining the algebraic properties of recently defined polynomial sequences, some important identities were given. The matrices of negative indices \textit{k-} Oresme polynomials was defined. Some sum formulas were given according to this definition.

Keywords

Matrices, Recurrences, Special sequences and polynomials

Thanks

Dear editor, thank your attention.

References

• [1] A. F. Horadam, Special properties of the sequenceWn(a;b; p;q) , Fibonacci Quart., 5(5) (1967), 424-434.
• [2] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, 3(3) (1965), Fibonacci Quart., 161-176.
• [3] A. F. Horadam, A generalized Fibonacci sequence, The American Mathematical Monthly, 68(5) (1961), 455-459.
• [4] Z. Akyuz, S. Halici, On some combinatorial identities involving the terms of generalized Fibonacci and Lucas sequences, Hacet. J. Math. Stat., 42(4) (2013), 431-435.
• [5] Z. Akyuz, S. Halici, Some identities deriving from the nth power of a special matrix, Adv. Difference Equ., (2012(1)), 1-6.
• [6] C. K. Cook, Some sums related to sums of Oresme numbers, In Applications of Fibonacci Numbers: Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci Numbers and Their Applications, (2004), 87-99.
• [7] James Mc. Laughlin, Combinatorial identities deriving from the nth power of a 2x2 matrix, Integers, 4 (2004), A19.
• [8] N. Oresme, Quaestiones super geometriam Euclidis, Brill Archive, 3 (1961).
• [9] A. F. Horadam, Oresme Numbers, Fibonacci Quart., 12(3) (1974), 267- 271.
• [10] G. Y. Senturk, N. Gurses, S. Yuce, A new look on Oresme numbers: dual-generalized complex component extension, In Conference Proceeding Science and Technology, 1(1) (2018), 254-265.
• [11] G. Cerda Morales, Oresme polynomials and their derivatives, arXiv preprint arXiv:1904.01165, (2019).
• [12] S. Halici, E. Sayin, Z. B. Gur, k- Oresme numbers and k- Oresme numbers with negative indices, ICMASE (2022), 211-223.
• [13] S. Halici, E. Sayin, On some k􀀀 Oresme hybrid numbers, Util. Math., 120, (2023), 1-11.
• [14] S. Halici, Z. B. Gur, E. Sayin, k- Oresme polynomials and their derivatives, ICMASE, (2022), 201-210.
• [15] S. Halici, Z. B. Gur, On some derivatives of k- Oresme polynomials, Bulletin of IMVI, 13(1) (2023), 41-50.
• [16] Y. Soykan, A study on generalized p- Oresme numbers, Asian Journal of Advanced Research and Reports, 15(7) (2021), 1-25.