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Year 2022, Volume: 10 Issue: 2, 269 - 275, 31.10.2022

Sıddıka Özkaldı Karakuş Semra Kaya Nurkan Murat Turan

Abstract

References

  • 1] Y. Alp and E. G Kocer, Some properties of Leonardo numbers, Konuralp J. Math. 9(1) (2021), 183-189.
  • [2] Y. Alp and E. G Kocer, Hybrid Leonardo numbers, Chaos, Solitons and Fractals 150 (2021), 111-128.
  • [3] F. R. V. Alves and P. Catarino, A forma matricial dos n ́umeros de Leonardo, Ciencia e natura, 42, (2020).
  • [4] P. Catarino and A. Borges, On Leonardo Numbers, Acta Mathematica Universitatis Comenianae, Vol:89, No.1 (2019), 75-86.
  • [5] P. Catarino and A. Borges, A Note on Incomplete Leonardo Numbers, Integers, Vol:20 (2020).
  • [6] W. K Clifford, Preliminary sketch of biquaternions, Proc London Mathematical Society. 4(64), (1873), 381-395.
  • [7] A. Cohen and M. Shoham, Application of hyper-dual numbers to multi-body kinematics. J. Mech. Rob. 8, (2015). doi: 10.1115/1.4030588.
  • [8] A. Cohen and M. Shoham, Application of hyper-dual numbers to rigid bodies equations of motion. J. Mech. Mach. Theory. 111, (2017), 76-84 .
  • [9] J. A. Fike, Numerically exact derivative calculations using hyper-dual numbers, 3rd Annual Student Joint Workshop in Simulation-Based Engineering and Design, (2009).
  • [10] J. A. Fike and J. J. Alonso, The development of hyper-dual numbers for exact second-derivative calculations, 49th AIAA Aerodpace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. (2011), 4-7.
  • [11] S. Halici, On Fibonacci quaternions, Adv. Appl. Clifford Algebras, 22, (2012) 321-327.
  • [12] Hoggatt V. E., Fibonacci and Lucas Numbers, A publication of the Fibonacci Association University of Santa Clara, Santa Clara, Houghton Mifflin Company, 1969.
  • [13] A. F. Horadam, Basic properties of a certain generalized sequence of numbers. Fibonacci Q., 3 (1965), 161-176.
  • [14] C. Kızılates and T. Kone, On higher order Fibonacci quaternions, J. Anal. (2021), DOI: 10.1007/s41478-020-00295-1.
  • [15] Kızılates C, Kone T, On higher order Fibonacci hyper complex numbers, Chaos Solitons Fractals 148 (2021), 111044.
  • [16] Koshy T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons: Hoboken, NJ, USA, 2019.
  • [17] F. Kuruz, A. Dagdeviren and P. Catarino, On Leonardo Pisano Hybrinomials, Mathematics, 9 (2021), 2923, https:/doi.org/10.3390/math9222923
  • [18] S. K. Nurkan, I. A. Guven, Dual Fibonacci quaternions, Adv. Appl. Clifford Algebras, 25(2) (2015), 403-414.
  • [19] N. Omur, S. Koparal, On hyper-dual generalized Fibonacci numbers, Notes on Number Theory and Discrete Mathematics, 26(1) (2020), 191-198.
  • [20] A. G. Shannon, A note on generalized Leonardo numbers, Notes Number Theory Discrete Math 25(3) (2019), 97-101. doi: 10.7546/nntdm.2019.25.3.97-101.
  • [21] Sloane N. J. A., The on-line encyclopedia of integers sequences, Http.//oeis.org , 1964.
  • [22] Vajda S., Fibonacci and Lucas Numbers and the golden section, Ellis Horwood Limited Publ., England, 1989.

Hyper-Dual Leonardo Numbers

Year 2022, Volume: 10 Issue: 2, 269 - 275, 31.10.2022

Sıddıka Özkaldı Karakuş Semra Kaya Nurkan Murat Turan

Abstract

In the present paper, the hyper-dual Leonardo numbers will be introduced with the use of Leonardo numbers. Some algebraic properties of these numbers such as recurrence relation, generating function, Catalan's and Cassini's identity, Binet's formula, sum formulas will also be obtained.

Keywords

Fibonacci numbers Hyper-dual numbers Leonardo numbers

References

  • 1] Y. Alp and E. G Kocer, Some properties of Leonardo numbers, Konuralp J. Math. 9(1) (2021), 183-189.
  • [2] Y. Alp and E. G Kocer, Hybrid Leonardo numbers, Chaos, Solitons and Fractals 150 (2021), 111-128.
  • [3] F. R. V. Alves and P. Catarino, A forma matricial dos n ́umeros de Leonardo, Ciencia e natura, 42, (2020).
  • [4] P. Catarino and A. Borges, On Leonardo Numbers, Acta Mathematica Universitatis Comenianae, Vol:89, No.1 (2019), 75-86.
  • [5] P. Catarino and A. Borges, A Note on Incomplete Leonardo Numbers, Integers, Vol:20 (2020).
  • [6] W. K Clifford, Preliminary sketch of biquaternions, Proc London Mathematical Society. 4(64), (1873), 381-395.
  • [7] A. Cohen and M. Shoham, Application of hyper-dual numbers to multi-body kinematics. J. Mech. Rob. 8, (2015). doi: 10.1115/1.4030588.
  • [8] A. Cohen and M. Shoham, Application of hyper-dual numbers to rigid bodies equations of motion. J. Mech. Mach. Theory. 111, (2017), 76-84 .
  • [9] J. A. Fike, Numerically exact derivative calculations using hyper-dual numbers, 3rd Annual Student Joint Workshop in Simulation-Based Engineering and Design, (2009).
  • [10] J. A. Fike and J. J. Alonso, The development of hyper-dual numbers for exact second-derivative calculations, 49th AIAA Aerodpace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. (2011), 4-7.
  • [11] S. Halici, On Fibonacci quaternions, Adv. Appl. Clifford Algebras, 22, (2012) 321-327.
  • [12] Hoggatt V. E., Fibonacci and Lucas Numbers, A publication of the Fibonacci Association University of Santa Clara, Santa Clara, Houghton Mifflin Company, 1969.
  • [13] A. F. Horadam, Basic properties of a certain generalized sequence of numbers. Fibonacci Q., 3 (1965), 161-176.
  • [14] C. Kızılates and T. Kone, On higher order Fibonacci quaternions, J. Anal. (2021), DOI: 10.1007/s41478-020-00295-1.
  • [15] Kızılates C, Kone T, On higher order Fibonacci hyper complex numbers, Chaos Solitons Fractals 148 (2021), 111044.
  • [16] Koshy T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons: Hoboken, NJ, USA, 2019.
  • [17] F. Kuruz, A. Dagdeviren and P. Catarino, On Leonardo Pisano Hybrinomials, Mathematics, 9 (2021), 2923, https:/doi.org/10.3390/math9222923
  • [18] S. K. Nurkan, I. A. Guven, Dual Fibonacci quaternions, Adv. Appl. Clifford Algebras, 25(2) (2015), 403-414.
  • [19] N. Omur, S. Koparal, On hyper-dual generalized Fibonacci numbers, Notes on Number Theory and Discrete Mathematics, 26(1) (2020), 191-198.
  • [20] A. G. Shannon, A note on generalized Leonardo numbers, Notes Number Theory Discrete Math 25(3) (2019), 97-101. doi: 10.7546/nntdm.2019.25.3.97-101.
  • [21] Sloane N. J. A., The on-line encyclopedia of integers sequences, Http.//oeis.org , 1964.
  • [22] Vajda S., Fibonacci and Lucas Numbers and the golden section, Ellis Horwood Limited Publ., England, 1989.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sıddıka Özkaldı Karakuş

Semra Kaya Nurkan 0000-0001-6473-4458

Murat Turan 0000-0001-9684-7924

Publication Date October 31, 2022
Submission Date September 23, 2022
Acceptance Date October 18, 2022
Published in Issue Year 2022 Volume: 10 Issue: 2

Cite

APA Özkaldı Karakuş, S., Kaya Nurkan, S., & Turan, M. (2022). Hyper-Dual Leonardo Numbers. Konuralp Journal of Mathematics, 10(2), 269-275.
AMA Özkaldı Karakuş S, Kaya Nurkan S, Turan M. Hyper-Dual Leonardo Numbers. Konuralp J. Math. October 2022;10(2):269-275.
Chicago Özkaldı Karakuş, Sıddıka, Semra Kaya Nurkan, and Murat Turan. “Hyper-Dual Leonardo Numbers”. Konuralp Journal of Mathematics 10, no. 2 (October 2022): 269-75.
EndNote Özkaldı Karakuş S, Kaya Nurkan S, Turan M (October 1, 2022) Hyper-Dual Leonardo Numbers. Konuralp Journal of Mathematics 10 2 269–275.
IEEE S. Özkaldı Karakuş, S. Kaya Nurkan, and M. Turan, “Hyper-Dual Leonardo Numbers”, Konuralp J. Math., vol. 10, no. 2, pp. 269–275, 2022.
ISNAD Özkaldı Karakuş, Sıddıka et al. “Hyper-Dual Leonardo Numbers”. Konuralp Journal of Mathematics 10/2 (October 2022), 269-275.
JAMA Özkaldı Karakuş S, Kaya Nurkan S, Turan M. Hyper-Dual Leonardo Numbers. Konuralp J. Math. 2022;10:269–275.
MLA Özkaldı Karakuş, Sıddıka et al. “Hyper-Dual Leonardo Numbers”. Konuralp Journal of Mathematics, vol. 10, no. 2, 2022, pp. 269-75.
Vancouver Özkaldı Karakuş S, Kaya Nurkan S, Turan M. Hyper-Dual Leonardo Numbers. Konuralp J. Math. 2022;10(2):269-75.
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