Öz
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.
Anahtar Kelimeler
fibonacci sequences gaussian numbers recurrence relation oresme numbers
Etik Beyan
There are no ethical issues with the publication of this article.
Destekleyen Kurum
This paper was suported Pamukkale University with Project No: 2023FEBE002.
Proje Numarası
2023FEBE002
Kaynakça
- Akyuz, Z. (2013). Some identities and Fibonacci type polynomials containing terms of generalized Fibonacci and Lucas sequences [Doctoral dissertation, Sakarya University].
- Berzsenyi, G. (1977). Gaussian Fibonacci numbers. Fibonacci Quarterly, 15(3), 233-236. https://doi.org/10.1080/00150517.1977.12430445
- 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/
- 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
- 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
- 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
- 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
- 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
- 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
- Horadam, A. F. (1963). Complex Fibonacci Numbers and Fibonacci Quaternions, Amer. Math. Monthly, 70, 289-291. https://doi.org/10.2307/2313129
- 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
- Horadam, A. F. (1974). Oresme numbers. Fibonacci Quarterly ,12(3), 267–270. https://doi.org/10.1080/00150517.1974.12430733
- Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications. A.Wiley- Interscience Publication. https://doi.org/10.1002/9781118033067
- 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
- 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
- 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
Öz
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.
Anahtar Kelimeler
fibonacci dizileri gaussian sayıları tekrarlama bağıntısı oresme sayıları
Proje Numarası
2023FEBE002
Kaynakça
- Akyuz, Z. (2013). Some identities and Fibonacci type polynomials containing terms of generalized Fibonacci and Lucas sequences [Doctoral dissertation, Sakarya University].
- Berzsenyi, G. (1977). Gaussian Fibonacci numbers. Fibonacci Quarterly, 15(3), 233-236. https://doi.org/10.1080/00150517.1977.12430445
- 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/
- 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
- 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
- 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
- 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
- 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
- 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
- Horadam, A. F. (1963). Complex Fibonacci Numbers and Fibonacci Quaternions, Amer. Math. Monthly, 70, 289-291. https://doi.org/10.2307/2313129
- 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
- Horadam, A. F. (1974). Oresme numbers. Fibonacci Quarterly ,12(3), 267–270. https://doi.org/10.1080/00150517.1974.12430733
- Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications. A.Wiley- Interscience Publication. https://doi.org/10.1002/9781118033067
- 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
- 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
- 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
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi |
| Bölüm | Araştırma Makaleleri |
| Yazarlar | |
| Proje Numarası | 2023FEBE002 |
| Yayımlanma Tarihi | 31 Aralık 2024 |
| Gönderilme Tarihi | 4 Nisan 2024 |
| Kabul Tarihi | 2 Temmuz 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 14 Sayı: 2 |
