Araştırma Makalesi
Yıl 2023,
Sayı: 42, 74 - 85, 31.03.2023
Öz
Kaynakça
- A. Macfarlane, Hyperbolic Quaternions, Proceedings of the Royal Society of Edinburgh 23 (1902) 169–180.
- I. A. Kösal, A Note on Hyperbolic Quaternions, Universal Journal of Mathematics and Applications 1 (3) (2018) 155–159.
- M. Bilgin, S. Ersoy, Algebraic Properties of Bihyperbolic Numbers, Advances in Applied Clifford Algebras 30 (1) (2020) 1–17.
- S. Demir, M. Tanışlı, N. Candemir, Hyperbolic Quaternion Formulation of Electromagnetism, Advances in Applied Clifford Algebras 20 (3) (2010) 547–563.
- F. Kürüz, A. Dağdeviren, Matrices with Hyperbolic Number Entries, Turkish Journal of Mathematics and Computer Science 14 (2) 306–313.
- A. K. T. Assis, Perplex Numbers and Quaternions, International Journal of Mathematical Education in Science and Technology 22 (4) (1991) 555–562.
- T. Koshy, Fibonacci and Lucas Numbers with Applications, 2nd Edition, John Wiley & Sons, New Jersey, 2018.
- N. N. Vorobiev, Fibonacci Numbers, Springer, Basel, 2002.
- P. M. Catarino, A. Borges, On Leonardo Numbers, Acta Mathematica Universitatis Comenianae 89 (1) (2019) 75–86.
- A. Yasemin, E. G. Koçer, Some Properties of Leonardo Numbers, Konuralp Journal of Mathematics 9 (1) (2021) 183–189.
- A. Shannon, A Note on Generalized Leonardo Numbers, Notes on Number Theory and Discrete Mathematics 25 (3) (2019) 97–101.
- Y. Alp, E. G. Koçer, Hybrid Leonardo Numbers, Chaos, Solitons & Fractals 150 (2021) 111128 5 pages.
- F. Kürüz, A. Dağdeviren, P. Catarino, On Leonardo Pisano Hybrinomials, Mathematics 9 (22) (2021) 2923 9 pages.
- S. Ö. Karakuş, S. K. Nurkan, M. Turan, Hyper-Dual Leonardo Numbers, Konuralp Journal of Mathematics 3 (28) (2022) 458–465.
- A. Karataş, On Complex Leonardo Numbers, Notes on Number Theory and Discrete Mathematics 10 (2) (2022) 269–275.
- Y. Soykan, Generalized Edouard Numbers, International Journal of Advances in Applied Mathematics and Mechanics 3 (9) (2022) 41–52.
- Y. Soykan, Generalized Ernst Numbers, Asian Journal of Pure and Applied Mathematics 4 (3) (2022) 1–15.
- Y. Soykan, İ. Okumuş, E. Taşdemir, Generalized Pisano Numbers, Notes on Number Theory and Discrete Mathematics 28 (3) (2022) 477–490.
- F. T. Aydın, Circular-Hyperbolic Fibonacci Quaternions, Notes on Number Theory and Discrete Mathematics 26 (2) (2020) 167–176.
- A. Godase, Hyperbolic k-Fibonacci and k-Lucas Quaternions, The Mathematics Student 90 (1-2) (2021) 103–116.
- A. Daşdemir, On Hyperbolic Lucas Quaternions, Ars Combin 150 (2020) 77–84.
- A. Daşdemir, On Recursive Hyperbolic Fibonacci Quaternions, Communications in Advanced Mathematical Sciences 4 (4) (2021) 198–207.
- T. Yağmur, A Note on Hyperbolic (p, q)−Fibonacci Quaternions, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 (1) (2020) 880–890.
- A. Z. Azak, Some New Identities with respect to Bihyperbolic Fibonacci and Lucas Numbers, International Journal of Sciences: Basic and Applied Sciences 60 (2021) 14–37.
- T. Yağmur, On Generalized Bicomplex k-Fibonacci Numbers, Notes Number Theory Discrete Math 25 (2019) 132–133.
Yıl 2023,
Sayı: 42, 74 - 85, 31.03.2023
Öz
In this paper, we present a new definition, referred to as the Francois sequence, related to the Lucas-like form of the Leonardo sequence. We also introduce the hyperbolic Leonardo and hyperbolic Francois quaternions. Afterward, we derive the Binet-like formulas and their generating functions. Moreover, we provide some binomial sums, Honsberger-like, d’Ocagne-like, Catalan-like, and Cassini-like identities of the hyperbolic Leonardo quaternions and hyperbolic Francois quaternions that allow an understanding of the quaternions' properties and their relation to the Francois sequence and Leonardo sequence. Finally, considering the results presented in this study, we discuss the need for further research in this field.
Anahtar Kelimeler
Fibonacci numbers Leonardo numbers Lucas numbers Francois numbers hyperbolic quaternions
Kaynakça
- A. Macfarlane, Hyperbolic Quaternions, Proceedings of the Royal Society of Edinburgh 23 (1902) 169–180.
- I. A. Kösal, A Note on Hyperbolic Quaternions, Universal Journal of Mathematics and Applications 1 (3) (2018) 155–159.
- M. Bilgin, S. Ersoy, Algebraic Properties of Bihyperbolic Numbers, Advances in Applied Clifford Algebras 30 (1) (2020) 1–17.
- S. Demir, M. Tanışlı, N. Candemir, Hyperbolic Quaternion Formulation of Electromagnetism, Advances in Applied Clifford Algebras 20 (3) (2010) 547–563.
- F. Kürüz, A. Dağdeviren, Matrices with Hyperbolic Number Entries, Turkish Journal of Mathematics and Computer Science 14 (2) 306–313.
- A. K. T. Assis, Perplex Numbers and Quaternions, International Journal of Mathematical Education in Science and Technology 22 (4) (1991) 555–562.
- T. Koshy, Fibonacci and Lucas Numbers with Applications, 2nd Edition, John Wiley & Sons, New Jersey, 2018.
- N. N. Vorobiev, Fibonacci Numbers, Springer, Basel, 2002.
- P. M. Catarino, A. Borges, On Leonardo Numbers, Acta Mathematica Universitatis Comenianae 89 (1) (2019) 75–86.
- A. Yasemin, E. G. Koçer, Some Properties of Leonardo Numbers, Konuralp Journal of Mathematics 9 (1) (2021) 183–189.
- A. Shannon, A Note on Generalized Leonardo Numbers, Notes on Number Theory and Discrete Mathematics 25 (3) (2019) 97–101.
- Y. Alp, E. G. Koçer, Hybrid Leonardo Numbers, Chaos, Solitons & Fractals 150 (2021) 111128 5 pages.
- F. Kürüz, A. Dağdeviren, P. Catarino, On Leonardo Pisano Hybrinomials, Mathematics 9 (22) (2021) 2923 9 pages.
- S. Ö. Karakuş, S. K. Nurkan, M. Turan, Hyper-Dual Leonardo Numbers, Konuralp Journal of Mathematics 3 (28) (2022) 458–465.
- A. Karataş, On Complex Leonardo Numbers, Notes on Number Theory and Discrete Mathematics 10 (2) (2022) 269–275.
- Y. Soykan, Generalized Edouard Numbers, International Journal of Advances in Applied Mathematics and Mechanics 3 (9) (2022) 41–52.
- Y. Soykan, Generalized Ernst Numbers, Asian Journal of Pure and Applied Mathematics 4 (3) (2022) 1–15.
- Y. Soykan, İ. Okumuş, E. Taşdemir, Generalized Pisano Numbers, Notes on Number Theory and Discrete Mathematics 28 (3) (2022) 477–490.
- F. T. Aydın, Circular-Hyperbolic Fibonacci Quaternions, Notes on Number Theory and Discrete Mathematics 26 (2) (2020) 167–176.
- A. Godase, Hyperbolic k-Fibonacci and k-Lucas Quaternions, The Mathematics Student 90 (1-2) (2021) 103–116.
- A. Daşdemir, On Hyperbolic Lucas Quaternions, Ars Combin 150 (2020) 77–84.
- A. Daşdemir, On Recursive Hyperbolic Fibonacci Quaternions, Communications in Advanced Mathematical Sciences 4 (4) (2021) 198–207.
- T. Yağmur, A Note on Hyperbolic (p, q)−Fibonacci Quaternions, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 (1) (2020) 880–890.
- A. Z. Azak, Some New Identities with respect to Bihyperbolic Fibonacci and Lucas Numbers, International Journal of Sciences: Basic and Applied Sciences 60 (2021) 14–37.
- T. Yağmur, On Generalized Bicomplex k-Fibonacci Numbers, Notes Number Theory Discrete Math 25 (2019) 132–133.
Toplam 25 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Uygulamalı Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Mart 2023 |
| Gönderilme Tarihi | 4 Kasım 2022 |
| Yayımlandığı Sayı | Yıl 2023 Sayı: 42 |
Kaynak Göster
Cited By
Combinatorial approach on the recurrence sequences: An evolutionary historical discussion about numerical sequences and the notion of the board
International Electronic Journal of Mathematics Education
https://doi.org/10.29333/iejme/14387
- Makale Dosyaları
|