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On Bicomplex Jacobsthal-Lucas Numbers

Yıl 2020, Cilt: 3 Sayı: 3, 139 - 143, 29.12.2020

Serpil Halıcı

https://doi.org/10.33187/jmsm.810655
Cited By: 2

Öz

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.

Anahtar Kelimeler

Bicomplex number Jacobsthal sequence Recurrences

Kaynakça

  • [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.

Yıl 2020, Cilt: 3 Sayı: 3, 139 - 143, 29.12.2020

Serpil Halıcı

https://doi.org/10.33187/jmsm.810655
Cited By: 2

Öz

Teşekkür

İlginiz için teşekkür ederim.

Kaynakça

  • [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.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Serpil Halıcı 0000-0002-8071-0437

Yayımlanma Tarihi 29 Aralık 2020
Gönderilme Tarihi 14 Ekim 2020
Kabul Tarihi 28 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 3

Kaynak Göster

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. Aralık 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, sy. 3 (Aralık 2020): 139-43. https://doi.org/10.33187/jmsm.810655.
EndNote Halıcı S (01 Aralık 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, c. 3, sy. 3, ss. 139–143, 2020, doi: 10.33187/jmsm.810655.
ISNAD Halıcı, Serpil. “On Bicomplex Jacobsthal-Lucas Numbers”. Journal of Mathematical Sciences and Modelling 3/3 (Aralık 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, c. 3, sy. 3, 2020, ss. 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.

Cited By

https://doi.org/
On Hyperbolic Jacobsthal-Lucas Sequence
Fundamental Journal of Mathematics and Applications
https://doi.org/10.33401/fujma.958524
 Kapak Resmi İndir

29237    Journal of Mathematical Sciences and Modelling 29238

                   29233

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