De Moivre-Type Identities for the Pell Numbers
Yıl: 2021 Cilt: 13 Sayı: 1 Sayfa Aralığı: 63 - 67 Metin Dili: İngilizce DOI: 10.47000/tjmcs.835237 İndeks Tarihi: 29-07-2022
De Moivre-Type Identities for the Pell Numbers
Öz: This paper aims to present a method for constructing the second order Pell and Pell-Lucas numbers and the third order Pell and Pell-Lucas numbers.Moreover, we obtain the De Moivre-type identities for these numbers. In addition, we define a Pell sequence with new initial conditions and give some identities for these third order Pell numbers such as Binet's formulas, generating functions, sums.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Aydın, F. G., Köklü, K., Yüce, S., Generalized Dual Pell Quaternions, Notes on Number Theory and Discrete Mathematics, 23(4), (2017), 66–84.
- [2] Bicknell, M., Hoggatt, V. E., A primer for the Fibonacci Numbers, Santa Clara, Calif.: The Fibonacci Association, B-10(1972), 45.
- [3] Bruce, I., A Modified Tribonacci Sequence, The Fibonacci Quarterly 22, 3(1984), 244–246.
- [4] Ercolano, J., Matrix generators of Pell sequences, The Fibonacci Quarterly, 17 (1)(1979), 71–77.
- [5] Horadam, A. F., Pell identities, The Fibonacci Quarterly 26, 9 (3)(1971), 245–252.
- [6] Kılıç, E., Taşcı, D., The generalized Binet formula, representation and sums of the generalized order- Pell numbers, Taiwanese J. Math., 10 (6)(2006), 1661–1670.
- [7] Kılıç, E., The generalized order- k Fibonacci - Pell sequence by matrix methods, Journal of Computational and Applied Mathematics, 209(2)(2007), 133–145.
- [8] Pethö, A., The Pell sequence contains only trivial perfect powers, In Colloquia on Sets, Graphs and Numbers, Soc. Math., J´anos Bolyai, North-Holland, Amsterdam (1991), 561–568.
- [9] Pin-Yen, L., De Moivre-Type Identities for the Tribonacci Numbers, The Fibonacci Quarterly, 2(1988), 131–134.
- [10] Pin-Yen, L., De Moivre-Type Identities for the Tetranacci Numbers, In: Bergum G.E., Philippou A.N., Horadam A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht(1991), https://doi.org/10.1007/978-94-011-3586-324.
- [11] Sloane, N.J.A., The on-line encyclopedia of integer sequences, http://oeis.org/.
- [12] Soykan, Y., On Generalized third-order Pell numbers, Asian Journal of Advanced Research and Reports, 6(1)(2019), https://doi.org/10.9734/ajarr/2019/v6i130144, 1–18.
| APA | YAMAÇ AKBIYIK S, AKBIYIK M (2021). De Moivre-Type Identities for the Pell Numbers. , 63 - 67. 10.47000/tjmcs.835237 |
| Chicago | YAMAÇ AKBIYIK SEDA,AKBIYIK Mücahit De Moivre-Type Identities for the Pell Numbers. (2021): 63 - 67. 10.47000/tjmcs.835237 |
| MLA | YAMAÇ AKBIYIK SEDA,AKBIYIK Mücahit De Moivre-Type Identities for the Pell Numbers. , 2021, ss.63 - 67. 10.47000/tjmcs.835237 |
| AMA | YAMAÇ AKBIYIK S,AKBIYIK M De Moivre-Type Identities for the Pell Numbers. . 2021; 63 - 67. 10.47000/tjmcs.835237 |
| Vancouver | YAMAÇ AKBIYIK S,AKBIYIK M De Moivre-Type Identities for the Pell Numbers. . 2021; 63 - 67. 10.47000/tjmcs.835237 |
| IEEE | YAMAÇ AKBIYIK S,AKBIYIK M "De Moivre-Type Identities for the Pell Numbers." , ss.63 - 67, 2021. 10.47000/tjmcs.835237 |
| ISNAD | YAMAÇ AKBIYIK, SEDA - AKBIYIK, Mücahit. "De Moivre-Type Identities for the Pell Numbers". (2021), 63-67. https://doi.org/10.47000/tjmcs.835237 |
| APA | YAMAÇ AKBIYIK S, AKBIYIK M (2021). De Moivre-Type Identities for the Pell Numbers. Turkish Journal of Mathematics and Computer Science, 13(1), 63 - 67. 10.47000/tjmcs.835237 |
| Chicago | YAMAÇ AKBIYIK SEDA,AKBIYIK Mücahit De Moivre-Type Identities for the Pell Numbers. Turkish Journal of Mathematics and Computer Science 13, no.1 (2021): 63 - 67. 10.47000/tjmcs.835237 |
| MLA | YAMAÇ AKBIYIK SEDA,AKBIYIK Mücahit De Moivre-Type Identities for the Pell Numbers. Turkish Journal of Mathematics and Computer Science, vol.13, no.1, 2021, ss.63 - 67. 10.47000/tjmcs.835237 |
| AMA | YAMAÇ AKBIYIK S,AKBIYIK M De Moivre-Type Identities for the Pell Numbers. Turkish Journal of Mathematics and Computer Science. 2021; 13(1): 63 - 67. 10.47000/tjmcs.835237 |
| Vancouver | YAMAÇ AKBIYIK S,AKBIYIK M De Moivre-Type Identities for the Pell Numbers. Turkish Journal of Mathematics and Computer Science. 2021; 13(1): 63 - 67. 10.47000/tjmcs.835237 |
| IEEE | YAMAÇ AKBIYIK S,AKBIYIK M "De Moivre-Type Identities for the Pell Numbers." Turkish Journal of Mathematics and Computer Science, 13, ss.63 - 67, 2021. 10.47000/tjmcs.835237 |
| ISNAD | YAMAÇ AKBIYIK, SEDA - AKBIYIK, Mücahit. "De Moivre-Type Identities for the Pell Numbers". Turkish Journal of Mathematics and Computer Science 13/1 (2021), 63-67. https://doi.org/10.47000/tjmcs.835237 |
