Dergiler / Turkish Journal of Mathematics and Computer Science / 2025 / Volume: 17 Issue: 2

A New Perspective On Hyper Dual Fibonnaci And Hyper Dual Lucas Numbers

Murat Turan(BILECIK SEYH EDEBALI UNIVERSITY)0000-0001-9684-7924
Sıddıka Özkaldı Karakuş(BİLECİK ŞEYH EDEBALİ ÜNİVERSİTESİ)0000-0002-2699-4109
Sayfa
—
Yayın Tarihi
2025-12-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Using Binet’s formula, we obtained some sum formulas and specific identities.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we introduction hyper dual numbers with hyper dual Fibonacci and Lucas number coefficients .
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Temel Bulgular & Veri:Firstly, we obtained for these new number recurrence relation and Binet’s formula.
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Sonuç & Katkı:Using Binet’s formula, we obtained some sum formulas and specific identities.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fibonacci numbers · Lucas numbers · hyper-dual numbers

Abstract

In this paper, we introduction hyper dual numbers with hyper dual Fibonacci and Lucas number coefficients . Firstly, we obtained for these new number recurrence relation and Binet’s formula. Using Binet’s formula, we obtained some sum formulas and specific identities.

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Bu Makaleye Atıf Yap

Turan, M., Karakuş, S. Ö. (2025). A New Perspective On Hyper Dual Fibonnaci And Hyper Dual Lucas Numbers. Turkish Journal of Mathematics and Computer Science, Volume: 17 Issue: 2. https://doi.org/10.47000/tjmcs.1564888

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Kaynakça (41)

  1. Adler, S.L., Quaternionic Quantum Mechanics and Quantum Fields, Oxford University Press, New York, 88, 1995.
  2. Alp, Y., Koçer, E.G., Some properties of Leonardo numbers, Konuralp J. Math., 9(1)(2021), 183–189.
  3. Alp, Y., Koçer, E.G., Hybrid Leonardo numbers, Chaos, Solitons Fractals, 150(2021), 111–128.
  4. Andrews, G.E., Askey, R., Roy, R., Special Functions, Cambridge University Press, Cambridge, 71, 1999.
  5. Akkuş, İ., Kızılaslan, G., Quaternions: Quantum calculus approach with applications, Kuwait J. Sci., 46(4)(2019), 1–13.
  6. Arfken, G.B., Weber, H.J., Mathematical Methods for Physicists, American Association of Physics Teachers, 1999.
  7. Aydın Torunbalcı, F., Bicomplex Fibonacci quaternions, Chaos, Solitons Fractals, 106(2)(2018), 147–153.
  8. Aydın Torunbalcı, F., q-Fibonacci bicomplex and q-Lucas bicomplex numbers, Notes Number Theory Discrete Math., 28(2)(2022), 261–275.
  9. Aydın Torunbalcı, F., q-Leonardo bicomplex numbers, Konuralp J. Math., 11(2)(2023), 176–183.
  10. da Fonseca, C.M., Kızılateş, C., Saraiva, P., Shannon, A.G., Generalised Leonardo numbers, Logic J. IGPL, (2025).
  11. Catarino, P., Borges, A., On Leonardo numbers, Acta Math. Univ. Comenianae, 89(1)(2019), 75–86.
  12. Clifford, W.K., Preliminary sketch of biquaternions, Proc. London Math. Soc., 4(64)(1873), 381–395.
  13. Cohen, A., Shoham, M., Application of hyper-dual numbers to multi-body kinematics, J. Mech. Rob., 8(2015).
  14. Cohen, A., Shoham, M., Application of hyper-dual numbers to rigid bodies equations of motion, Mech. Mach. Theory, 111(2017), 76–84.
  15. Fike, J. A., Numerically exact derivative calculations using hyper-dual numbers, 3rd Annual Student Workshop in Simulation-Based Engineering and Design, (2009).
  16. Fike, J.A., Alonso, J.J., The development of hyper-dual numbers for exact second-derivative calculations, 49th AIAA Aerospace Sciences Meeting, (2011).
  17. Güven, İ.A., Nurkan, S.K., A new approach to Fibonacci, Lucas numbers and dual vectors, Adv. Appl. Clifford Algebras, 25(2015), 577–590.
  18. Halıcı, S., On Fibonacci quaternions, Adv. Appl. Clifford Algebras, 22(2012), 321–327.
  19. Halıcı, S., On complex Fibonacci quaternions, Adv. Appl. Clifford Algebras, 23(1)(2013), 105–112.
  20. Hoggatt, V.E., Fibonacci and Lucas Numbers, Fibonacci Association, Houghton Mifflin, (1969).
  21. Horadam, A.F., Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly, 70(3)(1963), 289–291.
  22. Horadam, A.F., Basic properties of a certain generalized sequence of numbers, Fibonacci Q., 3(1965), 161–176.
  23. Horadam, A.F., Quaternions recurrence relations, Ulam Quarterly, 2(2)(1993), 23–33.
  24. Iyer, M.R., A note on Fibonacci quaternions, Fibonacci Q., 7(3)(1969), 225–229.
  25. Iyer, M.R., Some results on Fibonacci quaternions, Fibonacci Q., 7(1969), 201–210.
  26. Kürüz, F., Dağdeviren, A., Catarino, P., On Leonardo Pisano hybrinomials, Mathematics, 9(2021), 2923.
  27. Kızılateş, C., Kone, T., On higher order Fibonacci hyper complex numbers, Chaos Solitons Fractals, 148(2021), 111044.
  28. Kızılateş, C., On quaternions with incomplete Fibonacci and Lucas numbers components, Appl. Math. Comput. Sci. Stat., 110(2022).
  29. Kızılateş, C., Du, W.-S., Terzioğlu, N., Chen, R.-C., New properties and matrix representations on higher-order generalized Fibonacci quaternions with q-integer components, Axioms, 13(2024), 677.
  30. Kızılateş, C., Polatlı, E., Terzioğlu, N., Du, W.-S., On higher-order generalized Fibonacci hybrid numbers with q-integer components, Symmetry, 17(2025), 584.
  31. Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Hoboken, NJ, (2019).
  32. Turan, M., Özkaldı Karakuş, S., Kaya Nurkan, S., A new perspective on bicomplex numbers with Leonardo number components, Commun. Fac. Sci. Univ. Ankara Ser. A1 Math. Stat., 72(2)(2023), 340–351.
  33. Nurkan, S.K., Güven, İ.A., Dual Fibonacci quaternions, Adv. Appl. Clifford Algebras, 25(2)(2015), 403–414.
  34. Nurkan, S.K., Güven, İ.A., A note on bicomplex Fibonacci and Lucas numbers, Int. J. Pure Appl. Math., 120(3)(2015), 365–377.
  35. Nurkan, S.K., Güven, İ.A., Ordered Leonardo quadruple numbers, Symmetry, 15(2023), 149.
  36. Omur, N., Koparal, S., On hyper-dual generalized Fibonacci numbers, Notes Number Theory Discrete Math., 26(1)(2020), 191–198.
  37. Shannon, A.G., A note on generalized Leonardo numbers, Notes Number Theory Discrete Math., 25(3)(2019), 97–101.
  38. Sloane, N.J.A., The On-line Encyclopedia of Integer Sequences, (1964), http://oeis.org.
  39. Vajda, S., Fibonacci and Lucas Numbers and the Golden Section, Ellis Horwood Ltd., England, 1989.
  40. Karakuş, S.Ö., Nurkan, S.K., Turan, M., Hyper-dual Leonardo numbers, Konuralp J. Math., 10(2)(2022), 269–275.
  41. Vajda, S.,Fibonacci and Lucas Numbers and the Golden Section, Ellis Horwood Limited Publ., England, 1989.