Dergiler / Konuralp Journal of Mathematics / 2022 / Volume: 10 Issue: 2

Hyper-Dual Leonardo Numbers

Sıddıka Özkaldı Karakuş(BILECIK SEYH EDEBALI UNIVERSITY)
Semra Kaya Nurkan(Uşak Üniversitesi, Uşak, Türkiye)0000-0001-6473-4458
Murat Turan(BILECIK SEYH EDEBALI UNIVERSITY)0000-0001-9684-7924
Sayfa
—
Yayın Tarihi
2022-10-31
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In the present paper, the hyper-dual Leonardo numbers will be introduced with the use of Leonardo numbers.
📊
Temel Bulgular & Veri:In the present paper, the hyper-dual Leonardo numbers will be introduced with the use of Leonardo numbers.
💡
Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fibonacci numbers · Hyper-dual numbers · Leonardo numbers

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.

🔖

Bu Makaleye Atıf Yap

Karakuş, S. Ö., Nurkan, S. K., Turan, M. (2022). Hyper-Dual Leonardo Numbers. Konuralp Journal of Mathematics, Volume: 10 Issue: 2. https://ajindex.com/articles/1521544

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (24)

  1. 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.
  23. A. Cohen and M. Shoham, Application of hyper-dual numbers to rigid bodies equations of motion. J. Mech. Mach. Theory. 111, (2017), 76-84.
  24. Sloane N. J. A., The on-line encyclopedia of integers sequences, Http.//oeis.org, 1964.