Research Article
Year 2023,
Volume: 72 Issue: 2, 407 - 416, 23.06.2023
Abstract
References
- Aşcı, M., Gürel, E., Gaussian Jacobsthal and Gaussian Jacobsthal Lucas numbers, Ars Combinatoria, 111 (2013), 53–63.
- Ascı, M., Gürel, E., Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials, Notes on Number Theory and Discrete Mathematics, 19(1) (2013), 25–36.
- Berzsenyi, G., Gaussian Fibonacci numbers, Fibonacci Quarterly, 15(3) (1997), 233–236.
- El-Mikkawy, M., Sogabe, T., A new family of k-Fibonacci numbers, Applied Mathematics and Computation, 215(12) (2010), 4456–4461. https://doi.org/10.1016/j.amc.2009.12.069
- Halıcı, S., Öz, S., On Gaussian Pell polynomials and their some properties, Palestine Journal of Mathematics, 7(1) (2018), 251–256.
- Halıcı, S., Öz, S., On some Gaussian Pell and Pell-Lucas numbers, Ordu University Journal of Science and Technology, 6(1) (2016), 8–18.
- Horadam, A. F., Complex Fibonacci numbers and Fibonacci quaternions, The American Mathematical Monthly, 70(3) (1963), 289–291. https://doi.org/10.2307/2313129
- Jordan, J. H., Gaussian Fibonacci and Lucas numbers, Fibonacci Quarterly, 3(4) (1965), 315–318.
- Kaya, A., Özimamoğlu, H., On a new class of the generalized Gauss k-Pell numbers and their polynomials, Notes on Number Theory and Discrete Mathematics, 28(4) (2022), 593–602. https://doi.org/10.7546/nntdm.2022.28.4.593-602
- Özkan, E., Taştan, M., A new families of Gauss k-Jacobsthal numbers and Gauss k-Jacobsthal-Lucas numbers and their polynomials, Journal of Science and Arts., 4(53) (2020), 893–908. https://doi.org/10.46939/j.sci.arts-20.4-a10
- Özkan, E., Taştan, M., On a new family of Gauss k-Lucas numbers and their polynomials, Asian-European Journal of Mathematics, 14(06) (2021), 2150101. https://doi.org/10.1142/S1793557121501011
- Özkan, E., Taştan, M., On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications, Communications in Algebra, 48(3) (2020), 952–960. https://doi.org/10.1080/00927872.2019.1670193
- Taş, S., A new family of k-Gaussian Fibonacci numbers, Journal of Balıkesır University Institute of Science and Technology, 21(1) (2019), 184–189. https://doi.org/10.25092/baunfbed.542440
- Taştan, M., Özkan, E., On the Gauss k-Fibonacci polynomials, Electronic Journal of Mathematical Analysis and Applications, 9(1) (2021), 124–130.
- Yağmur, T., Gaussian Pell-Lucas polynomials, Communications in Mathematics and Applications, 10(4) (2019), 673–679. https://doi.org/10.26713/cma.v10i4.804
Year 2023,
Volume: 72 Issue: 2, 407 - 416, 23.06.2023
Abstract
In this paper, we generalize the known Gaussian Pell-Lucas numbers, and call such numbers as the generalized Gaussian k-Pell-Lucas numbers. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas numbers and the known Gaussian Pell-Lucas numbers. We generalize the known Gaussian Pell-Lucas polynomials, and call such polynomials as the generalized Gaussian k-Pell-Lucas polynomials. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas polynomials and the known Gaussian Pell-Lucas polynomials. In addition, we present the new generalizations of these numbers and polynomials in matrix form. Then, we get Cassini’s identities for these numbers and polynomials.
References
- Aşcı, M., Gürel, E., Gaussian Jacobsthal and Gaussian Jacobsthal Lucas numbers, Ars Combinatoria, 111 (2013), 53–63.
- Ascı, M., Gürel, E., Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials, Notes on Number Theory and Discrete Mathematics, 19(1) (2013), 25–36.
- Berzsenyi, G., Gaussian Fibonacci numbers, Fibonacci Quarterly, 15(3) (1997), 233–236.
- El-Mikkawy, M., Sogabe, T., A new family of k-Fibonacci numbers, Applied Mathematics and Computation, 215(12) (2010), 4456–4461. https://doi.org/10.1016/j.amc.2009.12.069
- Halıcı, S., Öz, S., On Gaussian Pell polynomials and their some properties, Palestine Journal of Mathematics, 7(1) (2018), 251–256.
- Halıcı, S., Öz, S., On some Gaussian Pell and Pell-Lucas numbers, Ordu University Journal of Science and Technology, 6(1) (2016), 8–18.
- Horadam, A. F., Complex Fibonacci numbers and Fibonacci quaternions, The American Mathematical Monthly, 70(3) (1963), 289–291. https://doi.org/10.2307/2313129
- Jordan, J. H., Gaussian Fibonacci and Lucas numbers, Fibonacci Quarterly, 3(4) (1965), 315–318.
- Kaya, A., Özimamoğlu, H., On a new class of the generalized Gauss k-Pell numbers and their polynomials, Notes on Number Theory and Discrete Mathematics, 28(4) (2022), 593–602. https://doi.org/10.7546/nntdm.2022.28.4.593-602
- Özkan, E., Taştan, M., A new families of Gauss k-Jacobsthal numbers and Gauss k-Jacobsthal-Lucas numbers and their polynomials, Journal of Science and Arts., 4(53) (2020), 893–908. https://doi.org/10.46939/j.sci.arts-20.4-a10
- Özkan, E., Taştan, M., On a new family of Gauss k-Lucas numbers and their polynomials, Asian-European Journal of Mathematics, 14(06) (2021), 2150101. https://doi.org/10.1142/S1793557121501011
- Özkan, E., Taştan, M., On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications, Communications in Algebra, 48(3) (2020), 952–960. https://doi.org/10.1080/00927872.2019.1670193
- Taş, S., A new family of k-Gaussian Fibonacci numbers, Journal of Balıkesır University Institute of Science and Technology, 21(1) (2019), 184–189. https://doi.org/10.25092/baunfbed.542440
- Taştan, M., Özkan, E., On the Gauss k-Fibonacci polynomials, Electronic Journal of Mathematical Analysis and Applications, 9(1) (2021), 124–130.
- Yağmur, T., Gaussian Pell-Lucas polynomials, Communications in Mathematics and Applications, 10(4) (2019), 673–679. https://doi.org/10.26713/cma.v10i4.804
There are 15 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | June 23, 2023 |
| Submission Date | June 30, 2022 |
| Acceptance Date | January 1, 2023 |
| Published in Issue | Year 2023 Volume: 72 Issue: 2 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
