Research Article
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On certain bihypernomials related to Pell and Pell-Lucas numbers

Year 2022, Volume: 71 Issue: 2, 422 - 433, 30.06.2022
https://doi.org/10.31801/cfsuasmas.890932

Abstract

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.

References

  • 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.
Year 2022, Volume: 71 Issue: 2, 422 - 433, 30.06.2022
https://doi.org/10.31801/cfsuasmas.890932

Abstract

References

  • 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.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Anetta Szynal-lıana 0000-0001-5508-0640

İwona Wloch 0000-0002-9969-0827

Mirosław Liana 0000-0001-5801-1755

Publication Date June 30, 2022
Submission Date March 4, 2021
Acceptance Date November 2, 2021
Published in Issue Year 2022 Volume: 71 Issue: 2

Cite

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. June 2022;71(2):422-433. doi:10.31801/cfsuasmas.890932
Chicago Szynal-lıana, Anetta, İwona Wloch, and 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, no. 2 (June 2022): 422-33. https://doi.org/10.31801/cfsuasmas.890932.
EndNote Szynal-lıana A, Wloch İ, Liana M (June 1, 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, and M. Liana, “On certain bihypernomials related to Pell and Pell-Lucas numbers”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 2, pp. 422–433, 2022, doi: 10.31801/cfsuasmas.890932.
ISNAD Szynal-lıana, Anetta et al. “On Certain Bihypernomials Related to Pell and Pell-Lucas Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/2 (June 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 et al. “On Certain Bihypernomials Related to Pell and Pell-Lucas Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 2, 2022, pp. 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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