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Dergiler / Journal of Mathematical Sciences and Modelling / 2018 / Cilt: 1 - Sayı: 2

On fourth-order jacobsthal quaternions

Gamaliel CERDA-MORALES
Sayfa
73–79
Yayın Tarihi
2018-09-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

This generalizes some previous results given by Szynal-Liana and Wloch in [13], Torunbalci Aydin and Yüce in [14] and Cerda-Morales in [2].

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions.
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Temel Bulgular & Veri:In particular, we are interested in the generating function, Binet formula, explicit formula and some interesting results for fourth-order Jacobsthal quaternions and fourth-order Jacobsthal-Lucas quaternions.
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Sonuç & Katkı:This generalizes some previous results given by Szynal-Liana and Wloch in [13], Torunbalci Aydin and Yüce in [14] and Cerda-Morales in [2].
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fourth-order Jacobsthal number · Jacobsthal number · quaternion

Abstract

In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. In particular, we are interested in the generating function, Binet formula, explicit formula and some interesting results for fourth-order Jacobsthal quaternions and fourth-order Jacobsthal-Lucas quaternions. This generalizes some previous results given by Szynal-Liana and Wloch in [13], Torunbalci Aydin and Yüce in [14] and Cerda-Morales in [2].

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Bu Makaleye Atıf Yap

CERDA-MORALES, G. (2018). On fourth-order jacobsthal quaternions. Journal of Mathematical Sciences and Modelling, Cilt: 1 - Sayı: 2, 73–79. https://ajindex.com/articles/777571

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Kaynakça (14)

  1. P. Barry, Triangle geometry and Jacobsthal numbers, Irish Math. Soc. Bulletin 51 (2003), 45–57
  2. G. Cerda-Morales, Identities for Third Order Jacobsthal Quaternions, Adv. Appl. Clifford Algebras 27(2) (2017), 1043–1053
  3. C. K. Cook and M.R. Bacon, Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations, Annales Mathematicae et Informaticae 41 (2013), 27–39
  4. O. Deveci, E. Karaduman and G. Saˇglam, The Jacobsthal sequences in finite groups, Bull. Iranian Math. Soc. 42(1) (2016), 79–89
  5. S. Halici, On Fibonacci quaternions, Adv. Appl. Clifford Algebras 22 (2012), 321–327
  6. S. Halici, On complex Fibonacci quaternions, Adv. Appl. Clifford Algebras 23 (2013), 105–112
  7. A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Am. Math. Month. 70 (1963), 289–291
  8. A. F. Horadam, Quaternion recurrence relations, Ulam Quarterly 2 (1993), 23–33
  9. A. F. Horadam, Jacobsthal representation numbers, Fibonacci Quarterly 34 (1996), 40–54
  10. M. R. Iyer, A note on Fibonacci quaternions, Fibonacci Quaterly 7(3) (1969), 225–229
  11. D. Kalman, Generalized Fibonacci numbers by matrix methods, Fibonacci Quaterly 20(1) (1982), 73–76
  12. F. Köken and D. Bozkurt, On the Jacobsthal numbers by matrix methods, Int. J. Contemp. Math. Sci. 3 (2008), 605–614
  13. A. Szynal-Liana and I. Włoch, A Note on Jacobsthal Quaternions, Adv. Appl. Clifford Algebras 26 (2016), 441–447
  14. F. Torunbalci Aydin and S.Yüce, A new approach to Jacobsthal quaternions, FILOMAT 31 (2017), 5567–5579.