On hyper-dual generalized Fibonacci numbers

Neşe Ömür and Sibel Koparal
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 1, Pages 191-198
DOI: 10.7546/nntdm.2020.26.1.191-198
Download full paper: PDF, 168 Kb

Details

Authors and affiliations

Neşe Ömür
Department of Mathematics, University of Kocaeli
41380 Izmit, Kocaeli, Turkey

Sibel Koparal
Department of Mathematics, University of Kocaeli
41380 Izmit, Kocaeli, Turkey

Abstract

In this paper, we define hyper-dual generalized Fibonacci numbers. We give the Binet
formulae, the generating functions and some basic identities for these numbers.

Keywords

  • Second order linear recurrence
  • Hyper-dual generalized Fibonacci number

2010 Mathematics Subject Classification

  • 11B50
  • 11A07
  • 11B68

References

  1. Akkus, I., & Keçilioğlu, O. (2015). Split Fibonacci and Lucas octonions, Adv. Appl. Clifford Algebras, 25 (3), 517–525.
  2. Keçilioğlu, O., & Akkus, I. (2015). The Fibonacci octonions, Adv. Appl. Clifford Algebras, 25 (1), 151–158.
  3. Akyiğit, M., Köksal, H. H., & Tosun, M. (2014). Fibonacci generalized quaternions, Adv. Appl. Clifford Algebras, 24, 535–545.
  4. Clifford, W. K. (1873). Preliminary sketch of bi-quaternions, Proceeding of London Mathematical Society, 4 (64), 65, 361–395.
  5. Cohen, A., & Shoham, M. (2017). Application of hyper-dual numbers to rigid bodies equations of motion, Mechanism and Machine Theory, 111, 76–84.
  6. Cohen, A., & Shoham, M. Application of hyper-dual numbers to multi-body kinematics, ASME J. Mech. Robot, doi:10.1115/1.4030588.
  7. Kılıç, E., & Stanica, P. (2009). Factorizations and representations of second order linear recurrences with indices in arithmetic progressions, Bulletin of the Mexican Mathematical Society, 15 (1), 23–36.
  8. Fike, J. A. (2009). Numerically exact derivative calculations using hyper-dual numbers, 3rd Annual Student Joint Workshop in Simulation-Based Engineering and Design, 18 June 2009.
  9. Fike, J. A., & Alonso, J. J. (2011). The development of hyper-dual numbers for exact second-derivative calculations, 49th AIAA Aerospace Sciences Meeting, 4-7 January 2011, Article No. AIAA 2011-886, 17 pages.
  10. Fike, J. A., Jongsma, S., & Alonso, J. J. (2011). E van der Weida, Optimization with gradient and Hessian information calculated using hyper-dual numbers, 29 AIAA Applied Aerodynamics Conference, Honolulu, Article No. AIAA 2011-3807, 19 pages.
  11. Akkus, I., & Kızılaslan, G. (2018). On some properties of Tribonacci quaternions, An. Stiint. Univ. Ovidius Constanta Ser. Mat., 26 (3), 5–20.
  12. Halıcı, S. (2015). On Fibonacci quarternions, Adv. Appl. Clifford Algebras, 25, 577–590.
  13. Horadam, A. F. (1963). Complex Fibonacci numbers and Fibonacci quaternions, American Math. Monthly, 70, 289–291.
  14. Iyer, M. R. (1969.) Some results on Fibonacci quaternions, The Fibonacci Quart., 7 (2), 201–210.
  15. Nurkan, S. K., & Güven, I. A. (2015). Dual Fibonacci quaternions, Adv. Appl. Clifford Algebras, 25, 403–414.
  16. Veldkamp, G. R. (1976). On the use of dual numbers, vectors and matrices in instantaneous, spatial kinematics, Mechanism and Machine Theory, 11 (2), 141–156.
  17. Yaglom, I. M. (1979). A Simple Non-Euclidean Geometry and Its Physical Basis, Springer- Verlag, New York.

Related papers

Cite this paper

Ömür, N., & Koparal, S. (2020). On hyper-dual generalized Fibonacci numbers. Notes on Number Theory and Discrete Mathematics, 26(1), 191-198, doi: 10.7546/nntdm.2020.26.1.191-198.

Comments are closed.