On Bicomplex Jacobsthal-Lucas Numbers

Serpil Halıcı

doi:10.33187/jmsm.810655

EN

On Bicomplex Jacobsthal-Lucas Numbers

Abstract

In this study we introduced a sequence of bicomplex numbers whose coefficients are chosen from the sequence of Jacobsthal-Lucas numbers. We also present some identities about the known some fundamental identities such as the Cassini's, Catalan's and Vajda's identities.

Keywords

Bicomplex number, Jacobsthal sequence, Recurrences

Thanks

İlginiz için teşekkür ederim.

References

[1] S. Halici, On fibonacci quaternions. Adv. Appl. Clifford Algebr., 22(2) (2012), 321-327.
[2] S. Halici, On Complex Fibonacci Quaternions. Adv. Appl. Clifford Algebr., 23(1) (2013), 105-112.
[3] M. Akyigit, H. H. Kosal, M. Tosun, Fibonacci generalized quaternions, Adv. Appl. Clifford Algebr., 24(3) (2014), 631-641.
[4] J. Cockle, LII. On systems of algebra involving more than one imaginary; and on equations of the fifth degree. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 35(238) (1849), 434-437.
[5] C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici, Math. Ann., 40 (1892), 413-467.
[6] G. B. Price, An Introduction to Multicomplex Spaces and Functions, Monographs and Textbooks in Pure and Applied Mathematics, 140, Marcel Dekker, Inc., New York, 1991.
[7] G. Dragoni, Sulle funzioni olomorfe di una variable bicomplessa, Reale Acad.d’Italia Mem. Class Sci. Fic. Mat.Nat., 5 (1934),597-665.
[8] M. Futagawa, On the theory of functions of quaternary variable-I, Tohoku Math. J., 29 (1928), 175-222.
[9] A. A. Pogorui, R. M. Rodriguez-Dagnino, On the set of zeros of bicomplex polynomials, Complex Var. Elliptic Equ., 51 7 (2006), 725-730.
[10] J. Ryan, Complexified Clifford analysis, Complex Var. Elliptic Equ., 1 (1982), 119-149.

[11] S. Halici, On Bicomplex Fibonacci Numbers and Their Generalization, Models and Theories in Soc. Syst., Springer Nature, Studies in Systems, Decision and Control Series, 2019.
[12] M.E. Luna-Elizarraras, E. M. Shapiro, D. C. Struppa, A. Vajiac Bicomplex numbers and their elementary functions, Cubo (Temuco), 14(2) (2012), 61-80.
[13] Z. Cerin, Sums of squares and products of Jacobsthal numbers, J. Integer Seq., 10(07.2) (2007), 5.
[14] D. Rochon, M. Shapiro, On algebraic properties of bicomplex and hyperbolic numbers, An. Univ. Oradea Fasc. Mat., 11 (2004),71-110.
[15] S. Halici, S¸ . Curuk, On Some Matrix Representations of Bicomplex Numbers, Konuralp Journal of Mathematics, 7(2), (2019), 449-455.
[16] A. F. Horadam, Jacobsthal representation numbers, Significance, 2 (1996), 2-8.
[17] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly, 70(3) (1963), 289-291.
[18] A. Szynal-Liana, I. Włoch, A note on jacobsthal quaternions, Adv. Appl. Clifford Algebr., 26(1) (2016), 441-447.
[19] D. Savin, Some properties of Fibonacci numbers, Fibonacci octonions, and generalized Fibonacci-Lucas octonions, Adv. Difference Equ., 2015(1) (2015), 298.
[20] T. Koshy, Fibonacci and Lucas Numbers with Applications, Vol 1, John Wiley and Sons, 2001.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Serpil Halıcı ^*
0000-0002-8071-0437
Türkiye

Publication Date

December 29, 2020

Submission Date

October 14, 2020

Acceptance Date

December 28, 2020

Published in Issue

Year 2020 Volume: 3 Number: 3

DOI

https://doi.org/10.33187/jmsm.810655

IZ

https://izlik.org/JA63JE46KP

APA

Halıcı, S. (2020). On Bicomplex Jacobsthal-Lucas Numbers. Journal of Mathematical Sciences and Modelling, 3(3), 139-143. https://doi.org/10.33187/jmsm.810655

AMA

1.Halıcı S. On Bicomplex Jacobsthal-Lucas Numbers. Journal of Mathematical Sciences and Modelling. 2020;3(3):139-143. doi:10.33187/jmsm.810655

Chicago

Halıcı, Serpil. 2020. “On Bicomplex Jacobsthal-Lucas Numbers”. Journal of Mathematical Sciences and Modelling 3 (3): 139-43. https://doi.org/10.33187/jmsm.810655.

EndNote

Halıcı S (December 1, 2020) On Bicomplex Jacobsthal-Lucas Numbers. Journal of Mathematical Sciences and Modelling 3 3 139–143.

IEEE

[1]S. Halıcı, “On Bicomplex Jacobsthal-Lucas Numbers”, Journal of Mathematical Sciences and Modelling, vol. 3, no. 3, pp. 139–143, Dec. 2020, doi: 10.33187/jmsm.810655.

ISNAD

Halıcı, Serpil. “On Bicomplex Jacobsthal-Lucas Numbers”. Journal of Mathematical Sciences and Modelling 3/3 (December 1, 2020): 139-143. https://doi.org/10.33187/jmsm.810655.

JAMA

1.Halıcı S. On Bicomplex Jacobsthal-Lucas Numbers. Journal of Mathematical Sciences and Modelling. 2020;3:139–143.

MLA

Halıcı, Serpil. “On Bicomplex Jacobsthal-Lucas Numbers”. Journal of Mathematical Sciences and Modelling, vol. 3, no. 3, Dec. 2020, pp. 139-43, doi:10.33187/jmsm.810655.

Vancouver

1.Serpil Halıcı. On Bicomplex Jacobsthal-Lucas Numbers. Journal of Mathematical Sciences and Modelling. 2020 Dec. 1;3(3):139-43. doi:10.33187/jmsm.810655