Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
hyperbolic number; bihyperbolic number; Fibonacci number; Pell number; Jacobsthal number
hyperbolic number; bihyperbolic number; Fibonacci number; Pell number; Jacobsthal number
Summary:
In this paper we introduce bihyperbolic numbers of the Fibonacci type. We present some of their properties using matrix generators and idempotent representations.
References:
[1] Aydin F. T.: On bicomplex Pell and Pell–Lucas numbers. Communications in Advanced Mathematical Sciences 1 (2018), no. 2, 142–155. DOI 10.33434/cams.439752
[2] Bilgin M., Ersoy S.: Algebraic properties of bihyperbolic numbers. Adv. Appl. Clifford Algebr. 30 (2020), no. 1, Paper No. 13, 17 pages. DOI 10.1007/s00006-019-1036-2 | MR 4054825
[3] Bród D., Szynal-Liana A., Włoch I.: On some combinatorial properties of bihyperbolic numbers of the Fibonacci type. Math. Methods Appl. Sci. 44 (2021), no. 6, 4607–4615. DOI 10.1002/mma.7054 | MR 4235524
[4] Çimen C. B..Ipek A.: On Pell quaternions and Pell–Lucas quaternions. Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 39–51. DOI 10.1007/s00006-015-0571-8 | MR 3459988
[5] Halici S.: On Fibonacci quaternions. Adv. Appl. Clifford Algebr. 22 (2012), no. 2, 321–327. DOI 10.1007/s00006-011-0317-1 | MR 2930698
[6] Horadam A. F.: Complex Fibonacci numbers and Fibonacci quaternions. Amer. Math. Monthly 70 (1963), 289–291. DOI 10.2307/2313129 | MR 0146137
[7] Iyer M. R.: A note on Fibonacci quaternions. Fibonacci Quart. 7 (1969), no. 3, 225–229. MR 0255513
[8] Nurkan S. K., Güven .I. A.: A note on bicomplex Fibonacci and Lucas numbers. Int. J. Pure Appl. Math. 120 (2018), no. 3, 365–377.
[9] Pogorui A. A., Rodríguez-Dagnino R. M., Rodríguez-Said R. D.: On the set of zeros of bihyperbolic polynomials. Complex Var. Elliptic Equ. 53 (2008), no. 7, 685–690. DOI 10.1080/17476930801973014 | MR 2431350
[10] Rochon D., Shapiro M.: On algebraic properties of bicomplex and hyperbolic numbers. An. Univ. Oradea Fasc. Mat. 11 (2004), 71–110. MR 2127591
[11] Sobczyk G.: The hyperbolic number plane. The College Mathematics Journal 26 (1995), no. 4, 268–280. DOI 10.1080/07468342.1995.11973712
[12] Szynal-Liana A., Włoch I.: A note on Jacobsthal quaternions. Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 441–447. DOI 10.1007/s00006-015-0622-1 | MR 3460010
[13] Szynal-Liana A., Włoch I.: The Pell quaternions and the Pell octonions. Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 435–440. DOI 10.1007/s00006-015-0570-9 | MR 3460009
[14] Szynal-Liana A., Włoch I.: On Pell and Pell–Lucas hybrid numbers. Comment. Math. 58 (2018), no. 1–2, 11–17. MR 3904772
[15] Szynal-Liana A., Włoch I.: Hypercomplex Numbers of the Fibonacci Type. Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów, 2019.
[16] Szynal-Liana A., Włoch I.: On Jacobsthal and Jacobsthal–Lucas hybrid numbers. Ann. Math. Sil. 33 (2019), no. 1, 276–283. MR 3982598
[17] Szynal-Liana A., Włoch I.: The Fibonacci hybrid numbers. Util. Math. 110 (2019), 3–10. MR 3967948
Search
Partner of
