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.
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
On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials
Year 2023,
Volume: 72 Issue: 2, 407 - 416, 23.06.2023
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.
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.
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
Özimamoğlu, H., & Kaya, A. (2023). On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(2), 407-416. https://doi.org/10.31801/cfsuasmas.1138441
AMA
Özimamoğlu H, Kaya A. On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2023;72(2):407-416. doi:10.31801/cfsuasmas.1138441
Chicago
Özimamoğlu, Hayrullah, and Ahmet Kaya. “On a New Family of the Generalized Gaussian K-Pell-Lucas Numbers and Their Polynomials”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 2 (June 2023): 407-16. https://doi.org/10.31801/cfsuasmas.1138441.
EndNote
Özimamoğlu H, Kaya A (June 1, 2023) On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 2 407–416.
IEEE
H. Özimamoğlu and A. Kaya, “On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 2, pp. 407–416, 2023, doi: 10.31801/cfsuasmas.1138441.
ISNAD
Özimamoğlu, Hayrullah - Kaya, Ahmet. “On a New Family of the Generalized Gaussian K-Pell-Lucas Numbers and Their Polynomials”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/2 (June 2023), 407-416. https://doi.org/10.31801/cfsuasmas.1138441.
JAMA
Özimamoğlu H, Kaya A. On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:407–416.
MLA
Özimamoğlu, Hayrullah and Ahmet Kaya. “On a New Family of the Generalized Gaussian K-Pell-Lucas Numbers and Their Polynomials”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 2, 2023, pp. 407-16, doi:10.31801/cfsuasmas.1138441.
Vancouver
Özimamoğlu H, Kaya A. On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(2):407-16.