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Year 2024, Volume: 12 Issue: 1, 46 - 54, 30.04.2024

Fügen Torunbalcı Aydın

Abstract

References

  • [1] Hamilton, W. R.: Elements of Quaternions. Longmans, Green and Co., London, (1866)
  • [2] Horadam, A. F.: Complex Fibonacci Numbers and Fibonacci Quaternions. American Math. Monthly. 70 (3), 289-291 (1963)
  • [3] Halıcı S.: On Fibonacci Quaternions. Adv. Appl. Clifford Algebras. 22 (2), 321-327 (2013)
  • [4] E. Polatli, S. Kesim, On quaternions with generalized fibonacci and lucas number components, Advances in Difference Equations 2015 (1) (2015) 1–8.
  • [5] E. Polatlı, A generalization of fibonacci and lucas quaternions, Advances in Applied Clifford Algebras 26 (2016) 719–730.
  • [6] E. Tan, S. Yilmaz, M. Sahin, On a new generalization of fibonacci quaternions, Chaos, Solitons & Fractals 82 (2016) 1–4.
  • [7] M. Akyigit, H. H¨uda K¨osal, M. Tosun, Fibonacci generalized quaternions, Advances in Applied Clifford Algebras 24 (2014) 631–641.
  • [8] S. Halici, A. Karata¸s, On a generalization for fibonacci quaternions, Chaos, Solitons & Fractals 98 (2017) 178–182.
  • [9] A. Horadam, Quaternion recurrence relations, Ulam Quarterly 2 (2) (1993) 23–33.
  • [10] M. R. Iyer, A note on fibonacci quaternions, Fibonacci Quart 7 (3) (1969) 225–229.
  • [11] M. Ozvatan, Generalized golden-fibonacci calculus and applications, Ph.D. thesis, Izmir Institute of Technology (Turkey) (2018).
  • [12] C. Kizilates¸, T. Kone, On higher order fibonacci quaternions, The Journal of Analysis (2021) 1–12.
  • [13] M. Uysal, E. Ozkan, Higher-order jacobsthal–lucas quaternions, Axioms 11 (12) (2022) 671.
  • [14] E. O¨ zkan, M. Uysal, On quaternions with higher order jacobsthal numbers components, Gazi University Journal of Science (2023) 1–1.
  • [15] M. Ozdemir, Introduction to hybrid numbers, Advances in applied Clifford algebras 28 (2018) 1–32.
  • [16] A. Da˘gdeviren, F. K¨ur¨uz, On the horadam hybrid quaternions, arXiv preprint arXiv:2012.08277.
  • [17] M. d. S. MAngueria, F. Alves, P. Catarino, Hybrid quaternions of leonardo, Trends in Computational and Applied Mathematics 23 (2022) 51–62.

On Higher Order Lucas Hybrid Quaternions

Year 2024, Volume: 12 Issue: 1, 46 - 54, 30.04.2024

Fügen Torunbalcı Aydın

Abstract

In this article, we introduced higher order Lucas hybrid quaternions with the help of higher order Lucas numbers. We also examined some algebraic properties of these quaternions. By obtaining the recurrence relation, we found the Binet formula, the generating function and the exponential generating function. Finally, we calculated the Vajda identity for the higher order Lucas hybrid quaternions and obtained the Catalan, Cassini and d'Ocagne identities with the help of this identity.

Keywords

Fibonacci number Lucas number Hybrid number Higher order Lucas number Binet formula

References

  • [1] Hamilton, W. R.: Elements of Quaternions. Longmans, Green and Co., London, (1866)
  • [2] Horadam, A. F.: Complex Fibonacci Numbers and Fibonacci Quaternions. American Math. Monthly. 70 (3), 289-291 (1963)
  • [3] Halıcı S.: On Fibonacci Quaternions. Adv. Appl. Clifford Algebras. 22 (2), 321-327 (2013)
  • [4] E. Polatli, S. Kesim, On quaternions with generalized fibonacci and lucas number components, Advances in Difference Equations 2015 (1) (2015) 1–8.
  • [5] E. Polatlı, A generalization of fibonacci and lucas quaternions, Advances in Applied Clifford Algebras 26 (2016) 719–730.
  • [6] E. Tan, S. Yilmaz, M. Sahin, On a new generalization of fibonacci quaternions, Chaos, Solitons & Fractals 82 (2016) 1–4.
  • [7] M. Akyigit, H. H¨uda K¨osal, M. Tosun, Fibonacci generalized quaternions, Advances in Applied Clifford Algebras 24 (2014) 631–641.
  • [8] S. Halici, A. Karata¸s, On a generalization for fibonacci quaternions, Chaos, Solitons & Fractals 98 (2017) 178–182.
  • [9] A. Horadam, Quaternion recurrence relations, Ulam Quarterly 2 (2) (1993) 23–33.
  • [10] M. R. Iyer, A note on fibonacci quaternions, Fibonacci Quart 7 (3) (1969) 225–229.
  • [11] M. Ozvatan, Generalized golden-fibonacci calculus and applications, Ph.D. thesis, Izmir Institute of Technology (Turkey) (2018).
  • [12] C. Kizilates¸, T. Kone, On higher order fibonacci quaternions, The Journal of Analysis (2021) 1–12.
  • [13] M. Uysal, E. Ozkan, Higher-order jacobsthal–lucas quaternions, Axioms 11 (12) (2022) 671.
  • [14] E. O¨ zkan, M. Uysal, On quaternions with higher order jacobsthal numbers components, Gazi University Journal of Science (2023) 1–1.
  • [15] M. Ozdemir, Introduction to hybrid numbers, Advances in applied Clifford algebras 28 (2018) 1–32.
  • [16] A. Da˘gdeviren, F. K¨ur¨uz, On the horadam hybrid quaternions, arXiv preprint arXiv:2012.08277.
  • [17] M. d. S. MAngueria, F. Alves, P. Catarino, Hybrid quaternions of leonardo, Trends in Computational and Applied Mathematics 23 (2022) 51–62.
There are 17 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Articles
Authors

Fügen Torunbalcı Aydın 0000-0001-9292-1832

Early Pub Date April 29, 2024
Publication Date April 30, 2024
Submission Date November 14, 2023
Acceptance Date December 11, 2023
Published in Issue Year 2024 Volume: 12 Issue: 1

Cite

APA Torunbalcı Aydın, F. (2024). On Higher Order Lucas Hybrid Quaternions. Konuralp Journal of Mathematics, 12(1), 46-54.
AMA Torunbalcı Aydın F. On Higher Order Lucas Hybrid Quaternions. Konuralp J. Math. April 2024;12(1):46-54.
Chicago Torunbalcı Aydın, Fügen. “On Higher Order Lucas Hybrid Quaternions”. Konuralp Journal of Mathematics 12, no. 1 (April 2024): 46-54.
EndNote Torunbalcı Aydın F (April 1, 2024) On Higher Order Lucas Hybrid Quaternions. Konuralp Journal of Mathematics 12 1 46–54.
IEEE F. Torunbalcı Aydın, “On Higher Order Lucas Hybrid Quaternions”, Konuralp J. Math., vol. 12, no. 1, pp. 46–54, 2024.
ISNAD Torunbalcı Aydın, Fügen. “On Higher Order Lucas Hybrid Quaternions”. Konuralp Journal of Mathematics 12/1 (April 2024), 46-54.
JAMA Torunbalcı Aydın F. On Higher Order Lucas Hybrid Quaternions. Konuralp J. Math. 2024;12:46–54.
MLA Torunbalcı Aydın, Fügen. “On Higher Order Lucas Hybrid Quaternions”. Konuralp Journal of Mathematics, vol. 12, no. 1, 2024, pp. 46-54.
Vancouver Torunbalcı Aydın F. On Higher Order Lucas Hybrid Quaternions. Konuralp J. Math. 2024;12(1):46-54.
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