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A new perspective on bicomplex numbers with Leonardo number components

Yıl 2023, Cilt: 72 Sayı: 2, 340 - 351, 23.06.2023
https://doi.org/10.31801/cfsuasmas.1181930

Öz

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.

Kaynakça

  • 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.
Yıl 2023, Cilt: 72 Sayı: 2, 340 - 351, 23.06.2023
https://doi.org/10.31801/cfsuasmas.1181930

Öz

Kaynakça

  • 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.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Murat Turan 0000-0001-9684-7924

Sıddıka Özkaldı Karakuş 0000-0002-2699-4109

Semra Kaya Nurkan 0000-0001-6473-4458

Yayımlanma Tarihi 23 Haziran 2023
Gönderilme Tarihi 30 Eylül 2022
Kabul Tarihi 20 Aralık 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 2

Kaynak Göster

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. Haziran 2023;72(2):340-351. doi:10.31801/cfsuasmas.1181930
Chicago Turan, Murat, Sıddıka Özkaldı Karakuş, ve 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, sy. 2 (Haziran 2023): 340-51. https://doi.org/10.31801/cfsuasmas.1181930.
EndNote Turan M, Özkaldı Karakuş S, Kaya Nurkan S (01 Haziran 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, ve S. Kaya Nurkan, “A new perspective on bicomplex numbers with Leonardo number components”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 2, ss. 340–351, 2023, doi: 10.31801/cfsuasmas.1181930.
ISNAD Turan, Murat vd. “A New Perspective on Bicomplex Numbers With Leonardo Number Components”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/2 (Haziran 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 vd. “A New Perspective on Bicomplex Numbers With Leonardo Number Components”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 72, sy. 2, 2023, ss. 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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