On some k- Oresme hybrid numbers including negative indices

Abstract

In this study, we define k-Oresme hybrid numbers including negative indices and examine their properties, using the theory of number systems created by choosing the coefficients from unique number sets. Moreover, we derive some fundamental identities related to these numbers.

Keywords

• Oresme numbers
• hybrid numbers
• recurrence relations

References

1. Cerda Morales, G., Oresme polynomials and their derivatives, arxiv preprint arXiv:1904.01165, (2019). https://doi.org/10.48550/arXiv.1904.01165
2. Cook, C.K., Some sums related to sums of Oresme numbers, Applications of Fibonacci Numbers, Proceedings of the Tenth International Research Conference on Fibonacci Numbers and Their Applications, Kluwer Academic Publishers, 9 (2004), 87–99. https://doi.org/10.1007/978-0-306-48517-6_10
3. Goy, T., Shattuck, M., Fibonacci and Lucas identities from Toeplitz–Hessenberg matrices, Applications and Applied Mathematics: An International Journal (AAM), 5 14(2), (2019). https://doi.org/10.22108/toc.2020.116257.1631
4. Halici, S., Sayın, E., Gur, Z. B., On k-Oresme Numbers with Negative Indices, Engineering (ICMASE 2022), 4-7 July 2022, Technical University of Civil Engineering Bucharest, Romania, 56 (2022). https://doi.org/10.1007/978-3031-21700-5_20
5. Halici, S., Gur, Z. B., Sayin, E., k- Oresme Polynomials and Their Derivatives Indices, Engineering (ICMASE 2022), 4-7 July 2022, Technical University of Civil Engineering Bucharest, Romania, 58 (2022). https://doi.org/10.1007/978-3-031-21700-5_19
6. Halici, S., Sayin, E., On some k-Oresme hybrid numbers, Utilitas Mathematica, 120 (2023), 1-11.
7. Horadam, A. F., Basic properties of a certain generalized sequence of numbers, The Fibonacci Quarterly, 3(3) (1965), 161-176. https://doi.org/10.1080/00150517.1965.12431416
8. Horadam, A. F., Oresme numbers, Fibonacci Quarterly, 12(3) (1974), 267-271.

9. Isbilir, Z., Gurses, N., Pentanacci and Pentanacci-Lucas hybrid numbers, Journal of Discrete Mathematical Sciences and Cryptography, (2021), 1-20. https://doi.org/10.1080/09720529.2021.1936899
10. Oresme, N., Quaestiones super geometriam Euclidis, Brill Archive, 3 (1961). https://doi.org/10.33434/cams.1444712
11. Ozdemir, M., Introduction to hybrid numbers, Advances in Applied Clifford Algebras, 28(1) (2018), 1-32. https://doi.org/10.1007/s00006-018-0833-3
12. Senturk, G. Y., Gurses, N., Yuce, S., A New Look on Oresme numbers: dual-generalized complex component extension, In Conference Proceedings of Science, 4(2) (2021), https://doi.org/206214.10.33434/cams.1444712
13. Szynal-Liana, A., The Horadam hybrid numbers, Discussiones Mathematicae: General Algebra and Applications, 38(1) (2018), 91-98. https://doi.org/10.7151/dmgaa.1287
14. Szynal-Liana, A., Wloch, I., Oresme hybrid numbers and hybrationals, Kragujevac Journal of Mathematics, 48(5) (2024), 747-753. https://doi.org/10.46793/KgJMat2405.747SL