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.
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
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.
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.