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Yıl 2021, Cilt: 4 Sayı: 4, 198 - 207, 27.12.2021

Ahmet Daşdemir

https://doi.org/10.33434/cams.997824
Cited By: 1

Öz

Destekleyen Kurum

Kastamonu University

Proje Numarası

KÜBAP-01/2018-8

Kaynakça

  • [1] W. R. Hamilton, Lectures on quaternions, Hodges and Smith, Dublin, 1853.
  • [2] J. H. Conway, Quaternions and octonions, A K Peters/CRC Press, Canada, 2003.
  • [3] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly, 70 (1963), 289-291.
  • [4] M. R. Iyer, Some results on Fibonacci quaternions, Fibonacci Quart., 2 (1969), 201-210.
  • [5] M. R. Iyer, A note on Fibonacci quaternions, Fibonacci Quart., 3 (1969), 225–229.
  • [6] C. Flaut, V. Shpakivskyi, On generalized Fibonacci quaternions and Fibonacci–Narayana quaternions, Adv. Appl. Clifford Alg., 23 (2013), 673-688.
  • [7] P. Catarino, A note on h(x)-Fibonacci quaternion polynomials, Chaos Solitons Fractals, 77 (2015), 1-5.
  • [8] J. L. Ramirez, Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions, An. St. Univ. Ovidius Constanta, 23 (2015), 201-212.
  • [9] A. P. Stakhov, I. S. Tkachenko, Hyperbolic Fibonacci trigonometry, Rep. Ukr. Acad. Sci., 208 (1993), 9-14.
  • [10] A. P. Stakhov, Hyperbolic Fibonacci and Lucas functions: A new mathematics for the living nature, ITI, Vinnitsa, 2003.
  • [11] A. P. Stakhov, B. Rozin, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23 (2005), 379-389.
  • [12] A. Das¸demir, On hyperbolic Lucas quaternions, Ars Combin., 150 (2020), 77-84.

On Recursive Hyperbolic Fibonacci Quaternions

Yıl 2021, Cilt: 4 Sayı: 4, 198 - 207, 27.12.2021

Ahmet Daşdemir

https://doi.org/10.33434/cams.997824
Cited By: 1

Öz

Many quaternions with the coefficients selected from special integer sequences such as Fibonacci and Lucas sequences have been investigated by a great number of researchers. This article presents new classes of quaternions whose components are composed of symmetrical hyperbolic Fibonacci functions. In addition, the Binet's formulas, certain generating matrices, generating functions, Cassini's and d'Ocagne's identities for these quaternions are given.

Anahtar Kelimeler

Binet Cassini Generating Matrix Hyperbolic Fibonacci functions Quaternion

Proje Numarası

KÜBAP-01/2018-8

Kaynakça

  • [1] W. R. Hamilton, Lectures on quaternions, Hodges and Smith, Dublin, 1853.
  • [2] J. H. Conway, Quaternions and octonions, A K Peters/CRC Press, Canada, 2003.
  • [3] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly, 70 (1963), 289-291.
  • [4] M. R. Iyer, Some results on Fibonacci quaternions, Fibonacci Quart., 2 (1969), 201-210.
  • [5] M. R. Iyer, A note on Fibonacci quaternions, Fibonacci Quart., 3 (1969), 225–229.
  • [6] C. Flaut, V. Shpakivskyi, On generalized Fibonacci quaternions and Fibonacci–Narayana quaternions, Adv. Appl. Clifford Alg., 23 (2013), 673-688.
  • [7] P. Catarino, A note on h(x)-Fibonacci quaternion polynomials, Chaos Solitons Fractals, 77 (2015), 1-5.
  • [8] J. L. Ramirez, Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions, An. St. Univ. Ovidius Constanta, 23 (2015), 201-212.
  • [9] A. P. Stakhov, I. S. Tkachenko, Hyperbolic Fibonacci trigonometry, Rep. Ukr. Acad. Sci., 208 (1993), 9-14.
  • [10] A. P. Stakhov, Hyperbolic Fibonacci and Lucas functions: A new mathematics for the living nature, ITI, Vinnitsa, 2003.
  • [11] A. P. Stakhov, B. Rozin, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23 (2005), 379-389.
  • [12] A. Das¸demir, On hyperbolic Lucas quaternions, Ars Combin., 150 (2020), 77-84.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Ahmet Daşdemir 0000-0001-8352-2020

Proje Numarası KÜBAP-01/2018-8
Yayımlanma Tarihi 27 Aralık 2021
Gönderilme Tarihi 20 Eylül 2021
Kabul Tarihi 1 Kasım 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 4

Kaynak Göster

APA Daşdemir, A. (2021). On Recursive Hyperbolic Fibonacci Quaternions. Communications in Advanced Mathematical Sciences, 4(4), 198-207. https://doi.org/10.33434/cams.997824
AMA Daşdemir A. On Recursive Hyperbolic Fibonacci Quaternions. Communications in Advanced Mathematical Sciences. Aralık 2021;4(4):198-207. doi:10.33434/cams.997824
Chicago Daşdemir, Ahmet. “On Recursive Hyperbolic Fibonacci Quaternions”. Communications in Advanced Mathematical Sciences 4, sy. 4 (Aralık 2021): 198-207. https://doi.org/10.33434/cams.997824.
EndNote Daşdemir A (01 Aralık 2021) On Recursive Hyperbolic Fibonacci Quaternions. Communications in Advanced Mathematical Sciences 4 4 198–207.
IEEE A. Daşdemir, “On Recursive Hyperbolic Fibonacci Quaternions”, Communications in Advanced Mathematical Sciences, c. 4, sy. 4, ss. 198–207, 2021, doi: 10.33434/cams.997824.
ISNAD Daşdemir, Ahmet. “On Recursive Hyperbolic Fibonacci Quaternions”. Communications in Advanced Mathematical Sciences 4/4 (Aralık 2021), 198-207. https://doi.org/10.33434/cams.997824.
JAMA Daşdemir A. On Recursive Hyperbolic Fibonacci Quaternions. Communications in Advanced Mathematical Sciences. 2021;4:198–207.
MLA Daşdemir, Ahmet. “On Recursive Hyperbolic Fibonacci Quaternions”. Communications in Advanced Mathematical Sciences, c. 4, sy. 4, 2021, ss. 198-07, doi:10.33434/cams.997824.
Vancouver Daşdemir A. On Recursive Hyperbolic Fibonacci Quaternions. Communications in Advanced Mathematical Sciences. 2021;4(4):198-207.

Cited By

On the Hyperbolic Leonardo and Hyperbolic Francois Quaternions
Journal of New Theory
https://doi.org/10.53570/jnt.1199465
 Kapak Resmi İndir

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