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Year 2022, Volume: 5 Issue: 1, 16 - 20, 01.03.2022
https://doi.org/10.33401/fujma.958524

Abstract

References

  • [1] A. F. Horadam, Jacobsthal represantation numbers, Fibonacci Quart., 34 (1996), 40-54.
  • [2] A. F. Horadam, Jacobsthal and Pell curves, Fibonacci Quart., 26 (1988), 79-83.
  • [3] A. F. Horadam, Jacobsthal representation polynomials, Fibonacci Quart., 35 (1997), 137-148.
  • [4] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3(3) (1965), 161-176.
  • [5] K. Atanassov, Remark on Jacobsthal numbers, Part 2. Notes Number Theory Discrete Math., 17(2) (2011), 37-39.
  • [6] K. Atanassov, Short remarks on Jacobsthal numbers, Notes Number Theory Discrete Math., 18(2) (2012), 63-64.
  • [7] M. C. Dikmen, Hyperbolic Jacobsthal numbers, Asian Res. J. Math., 4 (2019), 1-9.
  • [8] S. Tas, The Hyperbolic Quadrapell sequences, Eastern Anatolian J. Sci. VII(I) (2021), 25-29.
  • [9] M. A. G¨ung¨or, A. Cihan, On dual-hyperbolic numbers with generalized Fibonacci and Lucas numbers components, Fundamental J. Math. App., 2(2) (2019), 162-172
  • [10] A. P. Stakhov, Gazale formulas, a new class of the hyperbolic Fibonacci and Lucas functions, and the improved method of the ’Golden’ Cryptograph, Academy of Trinitarism, 77(6567) (2006), 1–32.
  • [11] A. P. Stakhov, I. S. Rozin, Hyperbolic Fibonacci trigonometry, Rep. Ukr. Acad. Sci., 208 (1993), 9–14, [In Russian].
  • [12] A. P. Stakhov, B. Tkachenko, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23 (2005), 379–389.
  • [13] F. Falcon, A. Plaza, The k-Fibonacci hyperbolic functions, Chaos Solitons Fractals, 38(2) (2008), 409–420.
  • [14] F. T. Aydın, Hyperbolic Fibonacci sequence, Univers. J. Math. Appl., 2(2) (2019), 59-64.
  • [15] S. Halıcı, On bicomplex Jacobsthal-Lucas numbers, J. Math. Sci. Model., 3(3) (2020), 139-143.
  • [16] H. Gargoubi, S. Kossentini, f-algebra structure on hyperbolic numbers, Adv. Appl. Clifford Algebras, 26(4) (2016), 1211-1233.
  • [17] A. E. Motter, A. F. Rosa, Hyperbolic calculus, Adv. App. Clifford Algebras, 8(1) (1998), 109-128.
  • [18] L. Barreira, L. H. Popescu, C. Valls, Hyperbolic sequences of linear operators and evolution maps, Milan J. Math., 84 (2016), 203-216.

On Hyperbolic Jacobsthal-Lucas Sequence

Year 2022, Volume: 5 Issue: 1, 16 - 20, 01.03.2022
https://doi.org/10.33401/fujma.958524

Abstract

In this study, we define the hyperbolic Jacobsthal-Lucas numbers and we obtain recurrence relations, Binet’s formula, generating function and the summation formulas for these numbers.

References

  • [1] A. F. Horadam, Jacobsthal represantation numbers, Fibonacci Quart., 34 (1996), 40-54.
  • [2] A. F. Horadam, Jacobsthal and Pell curves, Fibonacci Quart., 26 (1988), 79-83.
  • [3] A. F. Horadam, Jacobsthal representation polynomials, Fibonacci Quart., 35 (1997), 137-148.
  • [4] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3(3) (1965), 161-176.
  • [5] K. Atanassov, Remark on Jacobsthal numbers, Part 2. Notes Number Theory Discrete Math., 17(2) (2011), 37-39.
  • [6] K. Atanassov, Short remarks on Jacobsthal numbers, Notes Number Theory Discrete Math., 18(2) (2012), 63-64.
  • [7] M. C. Dikmen, Hyperbolic Jacobsthal numbers, Asian Res. J. Math., 4 (2019), 1-9.
  • [8] S. Tas, The Hyperbolic Quadrapell sequences, Eastern Anatolian J. Sci. VII(I) (2021), 25-29.
  • [9] M. A. G¨ung¨or, A. Cihan, On dual-hyperbolic numbers with generalized Fibonacci and Lucas numbers components, Fundamental J. Math. App., 2(2) (2019), 162-172
  • [10] A. P. Stakhov, Gazale formulas, a new class of the hyperbolic Fibonacci and Lucas functions, and the improved method of the ’Golden’ Cryptograph, Academy of Trinitarism, 77(6567) (2006), 1–32.
  • [11] A. P. Stakhov, I. S. Rozin, Hyperbolic Fibonacci trigonometry, Rep. Ukr. Acad. Sci., 208 (1993), 9–14, [In Russian].
  • [12] A. P. Stakhov, B. Tkachenko, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23 (2005), 379–389.
  • [13] F. Falcon, A. Plaza, The k-Fibonacci hyperbolic functions, Chaos Solitons Fractals, 38(2) (2008), 409–420.
  • [14] F. T. Aydın, Hyperbolic Fibonacci sequence, Univers. J. Math. Appl., 2(2) (2019), 59-64.
  • [15] S. Halıcı, On bicomplex Jacobsthal-Lucas numbers, J. Math. Sci. Model., 3(3) (2020), 139-143.
  • [16] H. Gargoubi, S. Kossentini, f-algebra structure on hyperbolic numbers, Adv. Appl. Clifford Algebras, 26(4) (2016), 1211-1233.
  • [17] A. E. Motter, A. F. Rosa, Hyperbolic calculus, Adv. App. Clifford Algebras, 8(1) (1998), 109-128.
  • [18] L. Barreira, L. H. Popescu, C. Valls, Hyperbolic sequences of linear operators and evolution maps, Milan J. Math., 84 (2016), 203-216.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sait Taş 0000-0002-9815-8732

Early Pub Date February 13, 2022
Publication Date March 1, 2022
Submission Date June 28, 2021
Acceptance Date December 23, 2021
Published in Issue Year 2022 Volume: 5 Issue: 1

Cite

APA Taş, S. (2022). On Hyperbolic Jacobsthal-Lucas Sequence. Fundamental Journal of Mathematics and Applications, 5(1), 16-20. https://doi.org/10.33401/fujma.958524
AMA Taş S. On Hyperbolic Jacobsthal-Lucas Sequence. Fundam. J. Math. Appl. March 2022;5(1):16-20. doi:10.33401/fujma.958524
Chicago Taş, Sait. “On Hyperbolic Jacobsthal-Lucas Sequence”. Fundamental Journal of Mathematics and Applications 5, no. 1 (March 2022): 16-20. https://doi.org/10.33401/fujma.958524.
EndNote Taş S (March 1, 2022) On Hyperbolic Jacobsthal-Lucas Sequence. Fundamental Journal of Mathematics and Applications 5 1 16–20.
IEEE S. Taş, “On Hyperbolic Jacobsthal-Lucas Sequence”, Fundam. J. Math. Appl., vol. 5, no. 1, pp. 16–20, 2022, doi: 10.33401/fujma.958524.
ISNAD Taş, Sait. “On Hyperbolic Jacobsthal-Lucas Sequence”. Fundamental Journal of Mathematics and Applications 5/1 (March 2022), 16-20. https://doi.org/10.33401/fujma.958524.
JAMA Taş S. On Hyperbolic Jacobsthal-Lucas Sequence. Fundam. J. Math. Appl. 2022;5:16–20.
MLA Taş, Sait. “On Hyperbolic Jacobsthal-Lucas Sequence”. Fundamental Journal of Mathematics and Applications, vol. 5, no. 1, 2022, pp. 16-20, doi:10.33401/fujma.958524.
Vancouver Taş S. On Hyperbolic Jacobsthal-Lucas Sequence. Fundam. J. Math. Appl. 2022;5(1):16-20.

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