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Year 2021, Volume: 4 Issue: 4, 198 - 207, 27.12.2021

Ahmet Daşdemir

https://doi.org/10.33434/cams.997824
Cited By: 1

Abstract

Supporting Institution

Kastamonu University

Project Number

KÜBAP-01/2018-8

References

  • [1] W. R. Hamilton, Lectures on quaternions, Hodges and Smith, Dublin, 1853.
  • [2] J. H. Conway, Quaternions and octonions, A K Peters/CRC Press, Canada, 2003.
  • [3] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly, 70 (1963), 289-291.
  • [4] M. R. Iyer, Some results on Fibonacci quaternions, Fibonacci Quart., 2 (1969), 201-210.
  • [5] M. R. Iyer, A note on Fibonacci quaternions, Fibonacci Quart., 3 (1969), 225–229.
  • [6] C. Flaut, V. Shpakivskyi, On generalized Fibonacci quaternions and Fibonacci–Narayana quaternions, Adv. Appl. Clifford Alg., 23 (2013), 673-688.
  • [7] P. Catarino, A note on h(x)-Fibonacci quaternion polynomials, Chaos Solitons Fractals, 77 (2015), 1-5.
  • [8] J. L. Ramirez, Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions, An. St. Univ. Ovidius Constanta, 23 (2015), 201-212.
  • [9] A. P. Stakhov, I. S. Tkachenko, Hyperbolic Fibonacci trigonometry, Rep. Ukr. Acad. Sci., 208 (1993), 9-14.
  • [10] A. P. Stakhov, Hyperbolic Fibonacci and Lucas functions: A new mathematics for the living nature, ITI, Vinnitsa, 2003.
  • [11] A. P. Stakhov, B. Rozin, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23 (2005), 379-389.
  • [12] A. Das¸demir, On hyperbolic Lucas quaternions, Ars Combin., 150 (2020), 77-84.

On Recursive Hyperbolic Fibonacci Quaternions

Year 2021, Volume: 4 Issue: 4, 198 - 207, 27.12.2021

Ahmet Daşdemir

https://doi.org/10.33434/cams.997824
Cited By: 1

Abstract

Many quaternions with the coefficients selected from special integer sequences such as Fibonacci and Lucas sequences have been investigated by a great number of researchers. This article presents new classes of quaternions whose components are composed of symmetrical hyperbolic Fibonacci functions. In addition, the Binet's formulas, certain generating matrices, generating functions, Cassini's and d'Ocagne's identities for these quaternions are given.

Keywords

Binet Cassini Generating Matrix Hyperbolic Fibonacci functions Quaternion

Project Number

KÜBAP-01/2018-8

References

  • [1] W. R. Hamilton, Lectures on quaternions, Hodges and Smith, Dublin, 1853.
  • [2] J. H. Conway, Quaternions and octonions, A K Peters/CRC Press, Canada, 2003.
  • [3] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly, 70 (1963), 289-291.
  • [4] M. R. Iyer, Some results on Fibonacci quaternions, Fibonacci Quart., 2 (1969), 201-210.
  • [5] M. R. Iyer, A note on Fibonacci quaternions, Fibonacci Quart., 3 (1969), 225–229.
  • [6] C. Flaut, V. Shpakivskyi, On generalized Fibonacci quaternions and Fibonacci–Narayana quaternions, Adv. Appl. Clifford Alg., 23 (2013), 673-688.
  • [7] P. Catarino, A note on h(x)-Fibonacci quaternion polynomials, Chaos Solitons Fractals, 77 (2015), 1-5.
  • [8] J. L. Ramirez, Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions, An. St. Univ. Ovidius Constanta, 23 (2015), 201-212.
  • [9] A. P. Stakhov, I. S. Tkachenko, Hyperbolic Fibonacci trigonometry, Rep. Ukr. Acad. Sci., 208 (1993), 9-14.
  • [10] A. P. Stakhov, Hyperbolic Fibonacci and Lucas functions: A new mathematics for the living nature, ITI, Vinnitsa, 2003.
  • [11] A. P. Stakhov, B. Rozin, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23 (2005), 379-389.
  • [12] A. Das¸demir, On hyperbolic Lucas quaternions, Ars Combin., 150 (2020), 77-84.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ahmet Daşdemir 0000-0001-8352-2020

Project Number KÜBAP-01/2018-8
Publication Date December 27, 2021
Submission Date September 20, 2021
Acceptance Date November 1, 2021
Published in Issue Year 2021 Volume: 4 Issue: 4

Cite

APA Daşdemir, A. (2021). On Recursive Hyperbolic Fibonacci Quaternions. Communications in Advanced Mathematical Sciences, 4(4), 198-207. https://doi.org/10.33434/cams.997824
AMA Daşdemir A. On Recursive Hyperbolic Fibonacci Quaternions. Communications in Advanced Mathematical Sciences. December 2021;4(4):198-207. doi:10.33434/cams.997824
Chicago Daşdemir, Ahmet. “On Recursive Hyperbolic Fibonacci Quaternions”. Communications in Advanced Mathematical Sciences 4, no. 4 (December 2021): 198-207. https://doi.org/10.33434/cams.997824.
EndNote Daşdemir A (December 1, 2021) On Recursive Hyperbolic Fibonacci Quaternions. Communications in Advanced Mathematical Sciences 4 4 198–207.
IEEE A. Daşdemir, “On Recursive Hyperbolic Fibonacci Quaternions”, Communications in Advanced Mathematical Sciences, vol. 4, no. 4, pp. 198–207, 2021, doi: 10.33434/cams.997824.
ISNAD Daşdemir, Ahmet. “On Recursive Hyperbolic Fibonacci Quaternions”. Communications in Advanced Mathematical Sciences 4/4 (December 2021), 198-207. https://doi.org/10.33434/cams.997824.
JAMA Daşdemir A. On Recursive Hyperbolic Fibonacci Quaternions. Communications in Advanced Mathematical Sciences. 2021;4:198–207.
MLA Daşdemir, Ahmet. “On Recursive Hyperbolic Fibonacci Quaternions”. Communications in Advanced Mathematical Sciences, vol. 4, no. 4, 2021, pp. 198-07, doi:10.33434/cams.997824.
Vancouver Daşdemir A. On Recursive Hyperbolic Fibonacci Quaternions. Communications in Advanced Mathematical Sciences. 2021;4(4):198-207.

Cited By

On the Hyperbolic Leonardo and Hyperbolic Francois Quaternions
Journal of New Theory
https://doi.org/10.53570/jnt.1199465
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