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A new perspective on bicomplex numbers with Leonardo number components

Year 2023, Volume: 72 Issue: 2, 340 - 351, 23.06.2023

Murat Turan Sıddıka Özkaldı Karakuş Semra Kaya Nurkan

https://doi.org/10.31801/cfsuasmas.1181930

Abstract

In the present paper, the bicomplex Leonardo numbers will be introduced with the use of Leonardo numbers and some important algebraic properties including recurrence relation, generating function, Catalan’s and Cassini’s identities, Binet’s formula, sum formulas will also be obtained.

Keywords

Fibonacci numbers bicomplex numbers Leonardo numbers

References

  • Alp, Y., Koçer, E. G., Some properties of Leonardo numbers, Konuralp J. Math., 9(1) (2021), 183–189.
  • Alp, Y., Koçer, E. G., Hybrid Leonardo numbers, Chaos, Solitons and Fractals, 150 (2021), 111–128. https://doi.org/10.1016/j.chaos.2021.111128
  • Alves, F. R. V., Catarino, P. M. M. C., A forma matricial dos n´umeros de Leonardo, Ciencia e natura, 42 (2020), 1–6. https://doi.org/10.5902/2179460X41839
  • Catarino, P., Borges, A., On Leonardo numbers, Acta Mathematica Universitatis Comenianae, 89(1) (2019), 75–86.
  • Catarino, P., Borges, A., A note on incomplete Leonardo numbers, Integers, 20(7) (2020).
  • Halıcı, S., On bicomplex Fibonacci numbers and their generalization, In Models and Theories in Social Systems, (2019), 509–524. https://doi.org/10.1007/978-3-030-00084-426
  • Hamilton, W. R., Lectures on Quaternions, Hodges and Smith, Dublin, 1853.
  • Hoggatt, V. E., Fibonacci and Lucas Numbers, A publication of the Fibonacci Association University of Santa Clara, Santa Clara, Houghton Mifflin Company, 1969.
  • Horadam, A. F., Basic properties of a certain generalized sequence of numbers, Fibonacci Quarterly 3 (1965), 161–176.
  • Kızılates C, Kone T. On higher order Fibonacci hyper complex numbers, Chaos Solitons Fractals, 148 (2021), 111044. https://doi.org/10.1016/j.chaos.2021.111044
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Hoboken, NJ, USA, 2019.
  • Kuruz, F., Dagdeviren, A., Catarino, P., On Leonardo Pisano hybrinomials, Mathematics, 9(22) (2021), 2923. https:/doi.org/10.3390/math9222923
  • Luna-Elizarraras, M. E., Shapiro, M., Struppa, D. C., Bicomplex numbers and their elementary functions, Cubo 14 (2012), 61–80.
  • Nurkan, S. K., Guven, I. A., A Note on bicomplex Fibonacci and Lucas numbers, International Journal of Pure and Applied Mathematics, 120(3) (2018), 365–377. https:/doi.org/10.12732/ijpam.v120i3.7
  • Price, G. B., An Introduction to Multicomplex Spaces and Functions, Monographs and Textbooks in Pure and Applied Mathematics, M. Dekker, New York, NY, USA, 1991.
  • Rochon, D., Shapiro, M., On algebraic properties of bicomplex and hyperbolic numbers, Anal. Univ. Oradea Fasc. Math., 11 (2004), 71–110.
  • Segre, C., The real representation of complex elements and hyperalgebraic entities (Italian), Math. Ann., 40 (1892), 413–467.
  • Shannon, A. G., A note on generalized Leonardo numbers, Notes Number Theory Discrete Math., 25(3) (2019), 97–101. https:/doi.org/10.7546/nntdm.2019.25.3.97-101.
  • Sloane, N. J. A., The On-line Encyclopedia of Integers Sequences. 1964.
  • Tan, E., Leung H. H., On Leonardo p-numbers, Integers, 23 (2023), 1-11. DOI: 10.5281/zenodo.7569221
  • Torunbalcı, A., Bicomplex Fibonacci quaternions, Chaos, Solitons and Fractals, 106 (2018), 147–153. https://doi.org/10.1016/j.chaos.2017.11.026
  • Vajda, S., Fibonacci and Lucas Numbers and The Golden Section, Ellis Horwood Limited Publ., England, 1989.

Year 2023, Volume: 72 Issue: 2, 340 - 351, 23.06.2023

Murat Turan Sıddıka Özkaldı Karakuş Semra Kaya Nurkan

https://doi.org/10.31801/cfsuasmas.1181930

Abstract

References

  • Alp, Y., Koçer, E. G., Some properties of Leonardo numbers, Konuralp J. Math., 9(1) (2021), 183–189.
  • Alp, Y., Koçer, E. G., Hybrid Leonardo numbers, Chaos, Solitons and Fractals, 150 (2021), 111–128. https://doi.org/10.1016/j.chaos.2021.111128
  • Alves, F. R. V., Catarino, P. M. M. C., A forma matricial dos n´umeros de Leonardo, Ciencia e natura, 42 (2020), 1–6. https://doi.org/10.5902/2179460X41839
  • Catarino, P., Borges, A., On Leonardo numbers, Acta Mathematica Universitatis Comenianae, 89(1) (2019), 75–86.
  • Catarino, P., Borges, A., A note on incomplete Leonardo numbers, Integers, 20(7) (2020).
  • Halıcı, S., On bicomplex Fibonacci numbers and their generalization, In Models and Theories in Social Systems, (2019), 509–524. https://doi.org/10.1007/978-3-030-00084-426
  • Hamilton, W. R., Lectures on Quaternions, Hodges and Smith, Dublin, 1853.
  • Hoggatt, V. E., Fibonacci and Lucas Numbers, A publication of the Fibonacci Association University of Santa Clara, Santa Clara, Houghton Mifflin Company, 1969.
  • Horadam, A. F., Basic properties of a certain generalized sequence of numbers, Fibonacci Quarterly 3 (1965), 161–176.
  • Kızılates C, Kone T. On higher order Fibonacci hyper complex numbers, Chaos Solitons Fractals, 148 (2021), 111044. https://doi.org/10.1016/j.chaos.2021.111044
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Hoboken, NJ, USA, 2019.
  • Kuruz, F., Dagdeviren, A., Catarino, P., On Leonardo Pisano hybrinomials, Mathematics, 9(22) (2021), 2923. https:/doi.org/10.3390/math9222923
  • Luna-Elizarraras, M. E., Shapiro, M., Struppa, D. C., Bicomplex numbers and their elementary functions, Cubo 14 (2012), 61–80.
  • Nurkan, S. K., Guven, I. A., A Note on bicomplex Fibonacci and Lucas numbers, International Journal of Pure and Applied Mathematics, 120(3) (2018), 365–377. https:/doi.org/10.12732/ijpam.v120i3.7
  • Price, G. B., An Introduction to Multicomplex Spaces and Functions, Monographs and Textbooks in Pure and Applied Mathematics, M. Dekker, New York, NY, USA, 1991.
  • Rochon, D., Shapiro, M., On algebraic properties of bicomplex and hyperbolic numbers, Anal. Univ. Oradea Fasc. Math., 11 (2004), 71–110.
  • Segre, C., The real representation of complex elements and hyperalgebraic entities (Italian), Math. Ann., 40 (1892), 413–467.
  • Shannon, A. G., A note on generalized Leonardo numbers, Notes Number Theory Discrete Math., 25(3) (2019), 97–101. https:/doi.org/10.7546/nntdm.2019.25.3.97-101.
  • Sloane, N. J. A., The On-line Encyclopedia of Integers Sequences. 1964.
  • Tan, E., Leung H. H., On Leonardo p-numbers, Integers, 23 (2023), 1-11. DOI: 10.5281/zenodo.7569221
  • Torunbalcı, A., Bicomplex Fibonacci quaternions, Chaos, Solitons and Fractals, 106 (2018), 147–153. https://doi.org/10.1016/j.chaos.2017.11.026
  • Vajda, S., Fibonacci and Lucas Numbers and The Golden Section, Ellis Horwood Limited Publ., England, 1989.
There are 22 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Murat Turan 0000-0001-9684-7924

Sıddıka Özkaldı Karakuş 0000-0002-2699-4109

Semra Kaya Nurkan 0000-0001-6473-4458

Publication Date June 23, 2023
Submission Date September 30, 2022
Acceptance Date December 20, 2022
Published in Issue Year 2023 Volume: 72 Issue: 2

Cite

APA Turan, M., Özkaldı Karakuş, S., & Kaya Nurkan, S. (2023). A new perspective on bicomplex numbers with Leonardo number components. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(2), 340-351. https://doi.org/10.31801/cfsuasmas.1181930
AMA Turan M, Özkaldı Karakuş S, Kaya Nurkan S. A new perspective on bicomplex numbers with Leonardo number components. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2023;72(2):340-351. doi:10.31801/cfsuasmas.1181930
Chicago Turan, Murat, Sıddıka Özkaldı Karakuş, and Semra Kaya Nurkan. “A New Perspective on Bicomplex Numbers With Leonardo Number Components”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 2 (June 2023): 340-51. https://doi.org/10.31801/cfsuasmas.1181930.
EndNote Turan M, Özkaldı Karakuş S, Kaya Nurkan S (June 1, 2023) A new perspective on bicomplex numbers with Leonardo number components. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 2 340–351.
IEEE M. Turan, S. Özkaldı Karakuş, and S. Kaya Nurkan, “A new perspective on bicomplex numbers with Leonardo number components”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 2, pp. 340–351, 2023, doi: 10.31801/cfsuasmas.1181930.
ISNAD Turan, Murat et al. “A New Perspective on Bicomplex Numbers With Leonardo Number Components”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/2 (June 2023), 340-351. https://doi.org/10.31801/cfsuasmas.1181930.
JAMA Turan M, Özkaldı Karakuş S, Kaya Nurkan S. A new perspective on bicomplex numbers with Leonardo number components. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:340–351.
MLA Turan, Murat et al. “A New Perspective on Bicomplex Numbers With Leonardo Number Components”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 2, 2023, pp. 340-51, doi:10.31801/cfsuasmas.1181930.
Vancouver Turan M, Özkaldı Karakuş S, Kaya Nurkan S. A new perspective on bicomplex numbers with Leonardo number components. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(2):340-51.

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

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