Research Article
Year 2025,
Volume: 30 Issue: 1, 92 - 101, 29.04.2025
Abstract
Bu makalede, kuantum tam sayıları içeren bileşenlere sahip yeni nesil tessarin sayı dizilerinin ayrıntılı bir çalışması sunulmaktadır. Ayrıca, Binet formülleri, Catalan, Cassini, D'ocagnes gibi çeşitli temel özdeşlikler tanımlanmıştır. Daha sonra, q-Fibonacci tessarine ve q-Lucas tessarine polinomları ve fonksiyon dizileri tanımlanmış ve bu diziler için çeşitli özellikler elde edilmiştir.
References
- Babadağ, F. (2017). Tessarines and homothetic exponential motions in 4-dimensional Euclidean space. Beykent University Journal of Science and Engineering, 10(1), 1-13.
- Babadağ, F., & Uslu, M. (2021). A new approach to Fibonacci tessarines with Fibonacci and Lucas number. Adıyaman University Journal of Science (ADYU J SCI), 11(2), 263-275. https://doi.org/10.37094/adyujsci.852037
- Babadağ, F. (2023). Quantum calculus approach to the dual number sequences. Research on Mathematics and Science- III, 3, 49-60. https://doi.org/10.58830/ozgur.pub252
- Cockle, J. (1849). III. On a new imaginary in algebra. The London Edinburgh and Dublin Philosophical Magazine and Journal of Science, 34(226), 37-47. https://doi.org/10.1080/14786444908646169
- Cockle, J. (1850). XXXI. On impossible equations, on impossible quantities, and on tessarines. The London Edinburgh and Dublin Philosophical Magazine and Journal of Science, 37(250), 281-283. https://doi.org/10.1080/14786445008646598
- Horadam, A. F. (1961). A generalized Fibonacci sequence. The American Mathematical Monthly, 68(5), 455-459. https://doi.org/10.1080/00029890.1961.11989696
- Horadam, A. F. (1963). Complex Fibonacci numbers and Fibonacci quaternions. The American Mathematical Monthly, 70(3), 289-291. https://doi.org/10.2307/2313129
- Kac, V., & Cheung, P. (2002). Quantum calculus. Springer. http://dx.doi.org/10.1007/978-1-4613-0071-7
- Kome, S., Kome, C., & Catarino, P. (2022). Quantum calculus approach to the dual bicomplex Fibonacci and Lucas number. Journal of Mathematical Extension, 6(2), 1-17. https://doi.org/10.30495/JME.2022.1906
- Koshy, T. (2018). Fibonacci and Lucas numbers with applications, 1. John Wiley Sons.
- Koshy, T. (2019). Fibonacci and Lucas numbers with applications, 2. John Wiley Sons
- Nalli, A., & Haukkanen, P. (2009). On generalized Fibonacci and Lucas polynomials. Chaos Solitons Fractals, 42, 3179-3186. https://doi.org/10.1016/j.chaos.2009.04.048
- Oduol, F., & Okoth, I. O. (2020). On generalized Fibonacci numbers. Communications in Advanced Mathematical Sciences, 3(4), 186-202. https://doi.org/10.33434/cams.771023
- Senna, F. R., & Valle, M. E. (2021). Tessarine and quaternion-valued deep neural networks for image classification. Proceedings of the National Meeting on Artificial and Computational Intelligence (ENIAC). https://doi.org/10.5753/eniac.2021.18266
- Stum, B., & Quiros, A. (2013). On quantum integers and rationals. Hal Open Science 649(13022), 107-130.
Year 2025,
Volume: 30 Issue: 1, 92 - 101, 29.04.2025
Abstract
This paper presents a detailed study of a new generation of tessarine number sequences with components including quantum integers Also, several fundamental identities are defined such as Binet formulas, Catalan, Cassini, D’ocagnes. After that, the q-Fibonacci tessarine and q-Lucas tessarine polynomials and function sequences are definedand obtained several properties for these sequences.
Keywords
q-Fibonacci tessarine number sequences q-Lucas tessarine number sequences Tessarine numbers
References
- Babadağ, F. (2017). Tessarines and homothetic exponential motions in 4-dimensional Euclidean space. Beykent University Journal of Science and Engineering, 10(1), 1-13.
- Babadağ, F., & Uslu, M. (2021). A new approach to Fibonacci tessarines with Fibonacci and Lucas number. Adıyaman University Journal of Science (ADYU J SCI), 11(2), 263-275. https://doi.org/10.37094/adyujsci.852037
- Babadağ, F. (2023). Quantum calculus approach to the dual number sequences. Research on Mathematics and Science- III, 3, 49-60. https://doi.org/10.58830/ozgur.pub252
- Cockle, J. (1849). III. On a new imaginary in algebra. The London Edinburgh and Dublin Philosophical Magazine and Journal of Science, 34(226), 37-47. https://doi.org/10.1080/14786444908646169
- Cockle, J. (1850). XXXI. On impossible equations, on impossible quantities, and on tessarines. The London Edinburgh and Dublin Philosophical Magazine and Journal of Science, 37(250), 281-283. https://doi.org/10.1080/14786445008646598
- Horadam, A. F. (1961). A generalized Fibonacci sequence. The American Mathematical Monthly, 68(5), 455-459. https://doi.org/10.1080/00029890.1961.11989696
- Horadam, A. F. (1963). Complex Fibonacci numbers and Fibonacci quaternions. The American Mathematical Monthly, 70(3), 289-291. https://doi.org/10.2307/2313129
- Kac, V., & Cheung, P. (2002). Quantum calculus. Springer. http://dx.doi.org/10.1007/978-1-4613-0071-7
- Kome, S., Kome, C., & Catarino, P. (2022). Quantum calculus approach to the dual bicomplex Fibonacci and Lucas number. Journal of Mathematical Extension, 6(2), 1-17. https://doi.org/10.30495/JME.2022.1906
- Koshy, T. (2018). Fibonacci and Lucas numbers with applications, 1. John Wiley Sons.
- Koshy, T. (2019). Fibonacci and Lucas numbers with applications, 2. John Wiley Sons
- Nalli, A., & Haukkanen, P. (2009). On generalized Fibonacci and Lucas polynomials. Chaos Solitons Fractals, 42, 3179-3186. https://doi.org/10.1016/j.chaos.2009.04.048
- Oduol, F., & Okoth, I. O. (2020). On generalized Fibonacci numbers. Communications in Advanced Mathematical Sciences, 3(4), 186-202. https://doi.org/10.33434/cams.771023
- Senna, F. R., & Valle, M. E. (2021). Tessarine and quaternion-valued deep neural networks for image classification. Proceedings of the National Meeting on Artificial and Computational Intelligence (ENIAC). https://doi.org/10.5753/eniac.2021.18266
- Stum, B., & Quiros, A. (2013). On quantum integers and rationals. Hal Open Science 649(13022), 107-130.
There are 15 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebra and Number Theory |
| Journal Section | Natural Sciences and Mathematics / Fen Bilimleri ve Matematik |
| Authors | |
| Publication Date | April 29, 2025 |
| Submission Date | December 3, 2024 |
| Acceptance Date | February 20, 2025 |
| Published in Issue | Year 2025 Volume: 30 Issue: 1 |
