Abstract
References
- Bergum, G.E., Hoggatt Jr., V.E., Irreducibility of Lucas and generalized Lucas polynomials, Fibonacci Quarterly, 12(1) (1974), 95-100.
- Catarino, P., On k-Pell hybrid numbers, Journal of Discrete Mathematical Sciences and Cryptography, 22(1) (2019), 83-89. https://doi.org/10.1080/09720529.2019.1569822
- Kızılates, C., A New Generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos, Solitons and Fractals, 130 (2020). https://doi.org/10.1016/j.chaos.2019.109449
- Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc., New York, 2001.
- Özdemir, M., Introduction to hybrid numbers, Advances in Applied Clifford Algebras, 28 (2018). https://doi.org/10.1007/s00006-018-0833-3
- Panwar, Y. K., Singh, M., Generalized bivariate Fibonacci-like polynomials, International Journal of Pure Mathematics, 1 (2014), 8-13.
- Swamy, M.N.S., Generalized Fibonacci and Lucas polynomials, and their associated diagonal polynomials, Fibonacci Quarterly, 37 (1999), 213-222.
- Szynal-Liana, A., Wloch, I., On Jacobsthal and Jacobsthal-Lucas hybrid numbers, Annales Mathematicae Silesianae, 33 (2019), 276-283. https://doi.org/10.2478/amsil-2018-0009
- Szynal-Liana, A., The Horadam hybrid numbers, Discussiones Mathematicae-General Algebra and Applications, 38 (2018), 91-98. https://doi.org/10.7151/dmgaa.1287
- Szynal-Liana, A., Wloch, I., On Pell and Pell-Lucas hybrid numbers, Commentationes Mathematicae, 58 (2018), 11-17. https://doi.org/10.14708/cm.v58i1-2.6364
- Szynal-Liana, A., Wloch, I., On Generalized Mersenne hybrid numbers, Annales Universitatis Mariae Curie-Sklodowska Lublin-Polonia, (2020), 77-84. https://doi.org/10.17951/ a.2020.74.1.77-84
- Szynal-Liana, A., Wloch, I., The Fibonacci hybrid numbers, Util. Math., 110 (2019), 3-10.
- Szynal-Liana, A., Wloch, I., Introduction to Fibonacci and Lucas hybrinomials, Complex Variables and Elliptic Equations, 65(10) (2020), 1736-1747. https://doi.org/10.1080/ 17476933.2019.1681416
- Sentürk, TC., Bilgici, G., Dasdemir, A., Ünal, Z., A study on Horadam hybrid numbers, Turkish Journal of Mathematics, 44 (2020), 1212-1221. https://doi.org/10.3906/mat-1908- 77
Abstract
Özdemir defined the hybrid numbers as a generalization of complex, hyperbolic and dual numbers. In this research, we define the generalized Lucas hybrinomials with two variables. Also, we get the Binet formula, generating function and some properties for the generalized Lucas hybrinomials. Moreover, Catalan's, Cassini's and d'Ocagne's identities for these hybrinomials are obtained. Lastly, by the help of the matrix theory we derive the matrix representation of the generalized Lucas hybrinomials.
Keywords
hybrid numbers Fibonacci numbers Lucas numbers polynomials hybrinomials recurrence relation
References
- Bergum, G.E., Hoggatt Jr., V.E., Irreducibility of Lucas and generalized Lucas polynomials, Fibonacci Quarterly, 12(1) (1974), 95-100.
- Catarino, P., On k-Pell hybrid numbers, Journal of Discrete Mathematical Sciences and Cryptography, 22(1) (2019), 83-89. https://doi.org/10.1080/09720529.2019.1569822
- Kızılates, C., A New Generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos, Solitons and Fractals, 130 (2020). https://doi.org/10.1016/j.chaos.2019.109449
- Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc., New York, 2001.
- Özdemir, M., Introduction to hybrid numbers, Advances in Applied Clifford Algebras, 28 (2018). https://doi.org/10.1007/s00006-018-0833-3
- Panwar, Y. K., Singh, M., Generalized bivariate Fibonacci-like polynomials, International Journal of Pure Mathematics, 1 (2014), 8-13.
- Swamy, M.N.S., Generalized Fibonacci and Lucas polynomials, and their associated diagonal polynomials, Fibonacci Quarterly, 37 (1999), 213-222.
- Szynal-Liana, A., Wloch, I., On Jacobsthal and Jacobsthal-Lucas hybrid numbers, Annales Mathematicae Silesianae, 33 (2019), 276-283. https://doi.org/10.2478/amsil-2018-0009
- Szynal-Liana, A., The Horadam hybrid numbers, Discussiones Mathematicae-General Algebra and Applications, 38 (2018), 91-98. https://doi.org/10.7151/dmgaa.1287
- Szynal-Liana, A., Wloch, I., On Pell and Pell-Lucas hybrid numbers, Commentationes Mathematicae, 58 (2018), 11-17. https://doi.org/10.14708/cm.v58i1-2.6364
- Szynal-Liana, A., Wloch, I., On Generalized Mersenne hybrid numbers, Annales Universitatis Mariae Curie-Sklodowska Lublin-Polonia, (2020), 77-84. https://doi.org/10.17951/ a.2020.74.1.77-84
- Szynal-Liana, A., Wloch, I., The Fibonacci hybrid numbers, Util. Math., 110 (2019), 3-10.
- Szynal-Liana, A., Wloch, I., Introduction to Fibonacci and Lucas hybrinomials, Complex Variables and Elliptic Equations, 65(10) (2020), 1736-1747. https://doi.org/10.1080/ 17476933.2019.1681416
- Sentürk, TC., Bilgici, G., Dasdemir, A., Ünal, Z., A study on Horadam hybrid numbers, Turkish Journal of Mathematics, 44 (2020), 1212-1221. https://doi.org/10.3906/mat-1908- 77
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | December 31, 2021 |
| Submission Date | January 5, 2021 |
| Acceptance Date | February 17, 2021 |
| Published in Issue | Year 2021 Volume: 70 Issue: 2 |
Cite
Cited By
Generalized bivariate conditional Fibonacci and Lucas hybrinomials
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
https://doi.org/10.31801/cfsuasmas.1249576
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
