SavedAdd your journal

Journals / Ordu Üniversitesi Bilim ve Teknoloji Dergisi / 2024 / Cilt: 14 Sayı: 2

On Some New Generalized Gaussian Oresme Numbers

Bazı Yeni Genelleştirilmiş Gaussian Oresme Sayıları

Elifcan Sayın(PAMUKKALE UNIVERSITY, INSTITUTE OF SCIENCE)0000-0001-5602-7681
Serpil Halıcı(PAMUKKALE UNIVERSITY)0000-0002-8071-0437
Pages
241–248
Publication Date
2024-12-31
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also obtained the relationship of these numbers with Gaussian Fibonacci numbers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we defined and examined a new generalization to a special sequence of rational numbers.
📊
Key Findings & Data:We gave the similarities and relationships of these newly defined Gaussian Oresme numbers with the generalized Fibonacci numbers and Lucas numbers existing in the literature.
💡
Conclusion & Impact:We also obtained the relationship of these numbers with Gaussian Fibonacci numbers.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:fibonacci dizileri · gaussian sayıları · tekrarlama bağıntısı

Abstract

In this study, we defined and examined a new generalization to a special sequence of rational numbers. We gave the similarities and relationships of these newly defined Gaussian Oresme numbers with the generalized Fibonacci numbers and Lucas numbers existing in the literature. Moreover, we have obtained some important identities provided by these numbers we have discussed. We also obtained the relationship of these numbers with Gaussian Fibonacci numbers.

Özet

Bu çalışmada rasyonel sayıların özel bir dizisine yönelik yeni bir genelleme tanımladık ve inceledik. Yeni tanımlanan bu Gaussian Oresme sayılarının literatürde var olan genelleştirilmiş Fibonacci sayıları ve Lucas sayıları ile benzerliklerini ve ilişkilerini verdik. Üstelik ele aldığımız bu sayıların sağladığı bazı önemli kimlikleri de elde ettik. Bu sayıların Gaussian Fibonacci sayılarıyla ilişkisini de elde ettik.

🔖

Cite This Article

Sayın, E., Halıcı, S., *, E. S. (2024). On Some New Generalized Gaussian Oresme Numbers. Ordu Üniversitesi Bilim ve Teknoloji Dergisi, Cilt: 14 Sayı: 2, 241–248. https://doi.org/10.54370/ordubtd.1459920

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. Akyuz, Z. (2013). Some identities and Fibonacci type polynomials containing terms of generalized Fibonacci and Lucas sequences [Doctoral dissertation, Sakarya University].
  2. Berzsenyi, G. (1977). Gaussian Fibonacci numbers. Fibonacci Quarterly, 15(3), 233-236. https://doi.org/10.1080/00150517.1977.12430445
  3. Cagman, A. (2021). Explicit solutions of powers of three as sums of three Pell numbers based on Baker’s type inequalities. Turkish J. Ineq, 5(1), 93-103. https://www.tjinequality.com/volume-5/issue-1/
  4. Cagman, A. (2021). An approach to Pillai's problem with the Pell sequence and the powers of 3. Miskolc Mathematical Notes, 22(2), 599-610. https://doi.org/10.18514/MMN.2021.3659
  5. Cagman, A. (2023). Repdigits as sums of three Half-companion Pell numbers. Miskolc Mathematical Notes, 24(2), 687-697. https://doi.org/10.18514/MMN.2023.4143
  6. Cook, C. K. (2004). 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. Dordrecht: Springer Netherlands, 87-99. https://doi.org/10.1007/978-0-306-48517-6_10
  7. Halici, S., & Sayin, E. (2023). On Some Gaussian Oresme Numbers, In International Conference on Mathematics and its Applications in Science and Engineering, 66. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-031-49218-1_25
  8. Halici, S., & Oz, S. (2016). On some Gaussian Pell and Pell-Lucas numbers. Ordu Üniversitesi Bilim ve Teknoloji Dergisi, 6(1), 8-18. https://dergipark.org.tr/tr/pub/ordubtd/issue/24680/261001
  9. Halici, S., & Curuk, S. (2020). On Dual k- Pell Bicomplex Numbers and Some Identities Including Them. Fundamental Journal of Mathematics and Applications, 3(1), 86-93. https://doi.org/10.33401/fujma.718298
  10. Horadam, A. F. (1963). Complex Fibonacci Numbers and Fibonacci Quaternions, Amer. Math. Monthly, 70, 289-291. https://doi.org/10.2307/2313129
  11. Horadam, A. F. (1965). Basic properties of a certain generalized sequence of numbers. Fibonacci Quarterly, 3(3), 161–176. https://doi.org/10.1080/00150517.1965.12431416
  12. Horadam, A. F. (1974). Oresme numbers. Fibonacci Quarterly,12(3), 267–270. https://doi.org/10.1080/00150517.1974.12430733
  13. Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications. A.Wiley- Interscience Publication. https://doi.org/10.1002/9781118033067
  14. Ozkan, E., & Tastan, M. (2020). On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications. Communications in Algebra, 48(3), 952960. https://doi.org/10.1080/00927872.2019.1670193
  15. Pethe, S., & Horadam, A. F. (1986). Generalised Gaussian Fibonacci numbers. Bulletin of the Australian Mathematical Society, 33(1), 37-48. https://doi.org/10.1017/S0004972700002847
  16. Yilmaz, F., & Ertas, A. (2023). On Quaternions with Gaussian Oresme Coefficients. Turkish Journal of Mathematics and Computer Science, 15(1), 192-202. https://doi.org/10.47000/tjmcs.1133973