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On certain bihypernomials related to Pell and Pell-Lucas numbers

Yıl 2022, Cilt: 71 Sayı: 2, 422 - 433, 30.06.2022
https://doi.org/10.31801/cfsuasmas.890932

Öz

The bihyperbolic numbers are extension of hyperbolic numbers to four dimensions. In this paper we introduce the concept of Pell and Pell-Lucas bihypernomials as a generalization of bihyperbolic Pell and Pell-Lucas numbers, respectively.

Kaynakça

  • Bilgin, M., Ersoy, S., Algebraic properties of bihyperbolic numbers, Adv. Appl. Clifford Algebr., 30(13) (2020). https://doi.org/10.1007/s00006-019-1036-2
  • Brod, D., Szynal-Liana, A., Wloch, I., Bihyperbolic numbers of the Fibonacci type and their idempotent representation, Comment. Math. Univ. Carolin., 62(4) (2021), 409-416. http://dx.doi.org/10.14712/1213-7243.2021.033
  • Brod, D., Szynal-Liana, A., Wloch, I., On some combinatorial properties of bihyperbolic numbers of the Fibonacci type, Math. Methods Appl. Sci., 44(6) (2021), 4607-4615. https://doi.org/10.1002/mma.7054
  • Halici, S., On the Pell polynomials, Appl. Math. Sci. (Ruse), 5(37) (2011), 1833–1838.
  • Horadam, A. F., Minmax Sequences for Pell Numbers, In: Bergum G.E., Philippou A.N., Horadam A.F. (eds) Applications of Fibonacci Numbers, Springer, Dordrecht, 1996.
  • Horadam, A. F., Pell identities, Fibonacci Quart., 9(3) (1971), 245–263.
  • Horadam, A. F., Mahon, Bro J. M., Pell and Pell-Lucas polynomials, Fibonacci Quart., 23(1) (1985), 7–20.
  • Horzum, T., Kocer, E. G., On some properties of Horadam polynomials, Int. Math. Forum, 25(4) (2009), 1243–1252.
  • Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
  • Rochon, D., Shapiro, M., On algebraic properties of bicomplex and hyperbolic numbers, An. Univ. Oradea Fasc. Mat., 11 (2004), 71–110.
  • Sobczyk, G., The hyperbolic number plane, College Math. J., 26(4) (1995). https://doi.org/10.1080/07468342.1995.11973712
  • Szynal-Liana, A., Wloch, I., On Pell and Pell-Lucas hybrid numbers, Comment. Math. Prace Mat., 58(1-2) (2018), 11–17. https://doi.org/10.14708/cm.v58i1-2.6364
  • Szynal-Liana, A., Wloch, I., The Pell quaternions and the Pell octonions, Adv. Appl. Clifford Algebr., 26 (2016), 435–440. https://doi.org/10.1007/s00006-015-0570-9
  • Szynal-Liana, A., Wloch, I., Hypercomplex Numbers of the Fibonacci Type, Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszow, 2019.
Yıl 2022, Cilt: 71 Sayı: 2, 422 - 433, 30.06.2022
https://doi.org/10.31801/cfsuasmas.890932

Öz

Kaynakça

  • Bilgin, M., Ersoy, S., Algebraic properties of bihyperbolic numbers, Adv. Appl. Clifford Algebr., 30(13) (2020). https://doi.org/10.1007/s00006-019-1036-2
  • Brod, D., Szynal-Liana, A., Wloch, I., Bihyperbolic numbers of the Fibonacci type and their idempotent representation, Comment. Math. Univ. Carolin., 62(4) (2021), 409-416. http://dx.doi.org/10.14712/1213-7243.2021.033
  • Brod, D., Szynal-Liana, A., Wloch, I., On some combinatorial properties of bihyperbolic numbers of the Fibonacci type, Math. Methods Appl. Sci., 44(6) (2021), 4607-4615. https://doi.org/10.1002/mma.7054
  • Halici, S., On the Pell polynomials, Appl. Math. Sci. (Ruse), 5(37) (2011), 1833–1838.
  • Horadam, A. F., Minmax Sequences for Pell Numbers, In: Bergum G.E., Philippou A.N., Horadam A.F. (eds) Applications of Fibonacci Numbers, Springer, Dordrecht, 1996.
  • Horadam, A. F., Pell identities, Fibonacci Quart., 9(3) (1971), 245–263.
  • Horadam, A. F., Mahon, Bro J. M., Pell and Pell-Lucas polynomials, Fibonacci Quart., 23(1) (1985), 7–20.
  • Horzum, T., Kocer, E. G., On some properties of Horadam polynomials, Int. Math. Forum, 25(4) (2009), 1243–1252.
  • Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
  • Rochon, D., Shapiro, M., On algebraic properties of bicomplex and hyperbolic numbers, An. Univ. Oradea Fasc. Mat., 11 (2004), 71–110.
  • Sobczyk, G., The hyperbolic number plane, College Math. J., 26(4) (1995). https://doi.org/10.1080/07468342.1995.11973712
  • Szynal-Liana, A., Wloch, I., On Pell and Pell-Lucas hybrid numbers, Comment. Math. Prace Mat., 58(1-2) (2018), 11–17. https://doi.org/10.14708/cm.v58i1-2.6364
  • Szynal-Liana, A., Wloch, I., The Pell quaternions and the Pell octonions, Adv. Appl. Clifford Algebr., 26 (2016), 435–440. https://doi.org/10.1007/s00006-015-0570-9
  • Szynal-Liana, A., Wloch, I., Hypercomplex Numbers of the Fibonacci Type, Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszow, 2019.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Anetta Szynal-lıana 0000-0001-5508-0640

İwona Wloch 0000-0002-9969-0827

Mirosław Liana 0000-0001-5801-1755

Yayımlanma Tarihi 30 Haziran 2022
Gönderilme Tarihi 4 Mart 2021
Kabul Tarihi 2 Kasım 2021
Yayımlandığı Sayı Yıl 2022 Cilt: 71 Sayı: 2

Kaynak Göster

APA Szynal-lıana, A., Wloch, İ., & Liana, M. (2022). On certain bihypernomials related to Pell and Pell-Lucas numbers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(2), 422-433. https://doi.org/10.31801/cfsuasmas.890932
AMA Szynal-lıana A, Wloch İ, Liana M. On certain bihypernomials related to Pell and Pell-Lucas numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2022;71(2):422-433. doi:10.31801/cfsuasmas.890932
Chicago Szynal-lıana, Anetta, İwona Wloch, ve Mirosław Liana. “On Certain Bihypernomials Related to Pell and Pell-Lucas Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, sy. 2 (Haziran 2022): 422-33. https://doi.org/10.31801/cfsuasmas.890932.
EndNote Szynal-lıana A, Wloch İ, Liana M (01 Haziran 2022) On certain bihypernomials related to Pell and Pell-Lucas numbers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 2 422–433.
IEEE A. Szynal-lıana, İ. Wloch, ve M. Liana, “On certain bihypernomials related to Pell and Pell-Lucas numbers”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 71, sy. 2, ss. 422–433, 2022, doi: 10.31801/cfsuasmas.890932.
ISNAD Szynal-lıana, Anetta vd. “On Certain Bihypernomials Related to Pell and Pell-Lucas Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/2 (Haziran 2022), 422-433. https://doi.org/10.31801/cfsuasmas.890932.
JAMA Szynal-lıana A, Wloch İ, Liana M. On certain bihypernomials related to Pell and Pell-Lucas numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:422–433.
MLA Szynal-lıana, Anetta vd. “On Certain Bihypernomials Related to Pell and Pell-Lucas Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 71, sy. 2, 2022, ss. 422-33, doi:10.31801/cfsuasmas.890932.
Vancouver Szynal-lıana A, Wloch İ, Liana M. On certain bihypernomials related to Pell and Pell-Lucas numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(2):422-33.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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