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On Bicomplex Jacobsthal-Lucas Numbers

Year 2020, Volume: 3 Issue: 3, 139 - 143, 29.12.2020
https://doi.org/10.33187/jmsm.810655

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.

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.
Year 2020, Volume: 3 Issue: 3, 139 - 143, 29.12.2020
https://doi.org/10.33187/jmsm.810655

Abstract

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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.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Serpil Halıcı 0000-0002-8071-0437

Publication Date December 29, 2020
Submission Date October 14, 2020
Acceptance Date December 28, 2020
Published in Issue Year 2020 Volume: 3 Issue: 3

Cite

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 Halıcı S. On Bicomplex Jacobsthal-Lucas Numbers. Journal of Mathematical Sciences and Modelling. December 2020;3(3):139-143. doi:10.33187/jmsm.810655
Chicago Halıcı, Serpil. “On Bicomplex Jacobsthal-Lucas Numbers”. Journal of Mathematical Sciences and Modelling 3, no. 3 (December 2020): 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 S. Halıcı, “On Bicomplex Jacobsthal-Lucas Numbers”, Journal of Mathematical Sciences and Modelling, vol. 3, no. 3, pp. 139–143, 2020, doi: 10.33187/jmsm.810655.
ISNAD Halıcı, Serpil. “On Bicomplex Jacobsthal-Lucas Numbers”. Journal of Mathematical Sciences and Modelling 3/3 (December 2020), 139-143. https://doi.org/10.33187/jmsm.810655.
JAMA 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, 2020, pp. 139-43, doi:10.33187/jmsm.810655.
Vancouver Halıcı S. On Bicomplex Jacobsthal-Lucas Numbers. Journal of Mathematical Sciences and Modelling. 2020;3(3):139-43.

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