Research Article
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Year 2021, Volume: 70 Issue: 2, 622 - 630, 31.12.2021

Emre Sevgi

https://doi.org/10.31801/cfsuasmas.854761
Cited By: 1

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

The generalized Lucas hybrinomials with two variables

Year 2021, Volume: 70 Issue: 2, 622 - 630, 31.12.2021

Emre Sevgi

https://doi.org/10.31801/cfsuasmas.854761
Cited By: 1

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
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Emre Sevgi 0000-0003-2711-9880

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

APA Sevgi, E. (2021). The generalized Lucas hybrinomials with two variables. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 622-630. https://doi.org/10.31801/cfsuasmas.854761
AMA Sevgi E. The generalized Lucas hybrinomials with two variables. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2021;70(2):622-630. doi:10.31801/cfsuasmas.854761
Chicago Sevgi, Emre. “The Generalized Lucas Hybrinomials With Two Variables”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 2 (December 2021): 622-30. https://doi.org/10.31801/cfsuasmas.854761.
EndNote Sevgi E (December 1, 2021) The generalized Lucas hybrinomials with two variables. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 622–630.
IEEE E. Sevgi, “The generalized Lucas hybrinomials with two variables”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 2, pp. 622–630, 2021, doi: 10.31801/cfsuasmas.854761.
ISNAD Sevgi, Emre. “The Generalized Lucas Hybrinomials With Two Variables”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (December 2021), 622-630. https://doi.org/10.31801/cfsuasmas.854761.
JAMA Sevgi E. The generalized Lucas hybrinomials with two variables. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:622–630.
MLA Sevgi, Emre. “The Generalized Lucas Hybrinomials With Two Variables”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 2, 2021, pp. 622-30, doi:10.31801/cfsuasmas.854761.
Vancouver Sevgi E. The generalized Lucas hybrinomials with two variables. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):622-30.

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Generalized bivariate conditional Fibonacci and Lucas hybrinomials
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