Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2021, Cilt: 70 Sayı: 2, 622 - 630, 31.12.2021

Emre Sevgi

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

Öz

Kaynakça

  • 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

Yıl 2021, Cilt: 70 Sayı: 2, 622 - 630, 31.12.2021

Emre Sevgi

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

Öz

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.

Anahtar Kelimeler

hybrid numbers Fibonacci numbers Lucas numbers polynomials hybrinomials recurrence relation

Kaynakça

  • 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
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Emre Sevgi 0000-0003-2711-9880

Yayımlanma Tarihi 31 Aralık 2021
Gönderilme Tarihi 5 Ocak 2021
Kabul Tarihi 17 Şubat 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 70 Sayı: 2

Kaynak Göster

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. Aralık 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, sy. 2 (Aralık 2021): 622-30. https://doi.org/10.31801/cfsuasmas.854761.
EndNote Sevgi E (01 Aralık 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., c. 70, sy. 2, ss. 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 (Aralık 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, c. 70, sy. 2, 2021, ss. 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.

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.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.