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BibTex RIS Kaynak Göster

Yıl 2019, Cilt: 2 Sayı: 3, 227 - 234, 30.09.2019

Fügen Torunbalcı Aydın

https://doi.org/10.33434/cams.542704
Cited By: 1

Öz

Kaynakça

  • [1] S. Falcon, A. Plaza, On the Fibonacci k-numbers, Chaos Solitons Fractals, 32(5) (2007), 1615-1624.
  • [2] S. Falcon, A. Plaza, The k-Fibonacci sequence and the pascal 2-triangle, Chaos Solitons Fractals, 33(1) (2007), 38-49.
  • [3] J. L. Ramirez, Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions, An. Univ. ”Ovidius” Constanta Ser. Mat., 23(2) (2015), 201-212.
  • [4] C. Segre, Le rappresentazioni reali delle forme complesse e gli ente iper-algebrici, Math. Ann., 40(3) (1892), 413-467.
  • [5] G. B. Price, An Introduction to Multicomplex Spaces and Functions, M. Dekker, 1991.
  • [6] P. Catarino, Bicomplex k-Pell quaternions, Comput. Methods Funct. Theory, 19(1) (2019), 65-76.
  • [7] F. Aydın, Torunbalcı, Bicomplex Fibonacci quaternions, Chaos Solitons Fractals, 106 (2018), 147-153.
  • [8] E. Kılıç, D. Tascı, P. Haukkanen, On the generalized Lucas sequence by Hessenberg matrices, Ars. Comb., 95 (2010), 383-395.

On the Bicomplex $k$-Fibonacci Quaternions

Yıl 2019, Cilt: 2 Sayı: 3, 227 - 234, 30.09.2019

Fügen Torunbalcı Aydın

https://doi.org/10.33434/cams.542704
Cited By: 1

Öz

In this paper, bicomplex $k$-Fibonacci quaternions are defined. Also, some algebraic properties of bicomplex $k$-Fibonacci quaternions are investigated. For example, the summation formula, generating functions, Binet's formula, the Honsberger identity, the d'Ocagne's identity, Cassini's identity, Catalan's identity for these quaternions are given. In the last part, a different way to find $n-th$ term of the bicomplex $k$-Fibonacci quaternion sequence was given using the determinant of a tridiagonal matrix.

Anahtar Kelimeler

Bicomplex number k-Fibonacci number Bicomplex Fibonacci quaternion Bicomplex k-Fibonacci quaternion Tridiagonal matrix

Kaynakça

  • [1] S. Falcon, A. Plaza, On the Fibonacci k-numbers, Chaos Solitons Fractals, 32(5) (2007), 1615-1624.
  • [2] S. Falcon, A. Plaza, The k-Fibonacci sequence and the pascal 2-triangle, Chaos Solitons Fractals, 33(1) (2007), 38-49.
  • [3] J. L. Ramirez, Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions, An. Univ. ”Ovidius” Constanta Ser. Mat., 23(2) (2015), 201-212.
  • [4] C. Segre, Le rappresentazioni reali delle forme complesse e gli ente iper-algebrici, Math. Ann., 40(3) (1892), 413-467.
  • [5] G. B. Price, An Introduction to Multicomplex Spaces and Functions, M. Dekker, 1991.
  • [6] P. Catarino, Bicomplex k-Pell quaternions, Comput. Methods Funct. Theory, 19(1) (2019), 65-76.
  • [7] F. Aydın, Torunbalcı, Bicomplex Fibonacci quaternions, Chaos Solitons Fractals, 106 (2018), 147-153.
  • [8] E. Kılıç, D. Tascı, P. Haukkanen, On the generalized Lucas sequence by Hessenberg matrices, Ars. Comb., 95 (2010), 383-395.
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Fügen Torunbalcı Aydın 0000-0002-4953-1078

Yayımlanma Tarihi 30 Eylül 2019
Gönderilme Tarihi 21 Mart 2019
Kabul Tarihi 2 Ağustos 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 3

Kaynak Göster

APA Torunbalcı Aydın, F. (2019). On the Bicomplex $k$-Fibonacci Quaternions. Communications in Advanced Mathematical Sciences, 2(3), 227-234. https://doi.org/10.33434/cams.542704
AMA Torunbalcı Aydın F. On the Bicomplex $k$-Fibonacci Quaternions. Communications in Advanced Mathematical Sciences. Eylül 2019;2(3):227-234. doi:10.33434/cams.542704
Chicago Torunbalcı Aydın, Fügen. “On the Bicomplex $k$-Fibonacci Quaternions”. Communications in Advanced Mathematical Sciences 2, sy. 3 (Eylül 2019): 227-34. https://doi.org/10.33434/cams.542704.
EndNote Torunbalcı Aydın F (01 Eylül 2019) On the Bicomplex $k$-Fibonacci Quaternions. Communications in Advanced Mathematical Sciences 2 3 227–234.
IEEE F. Torunbalcı Aydın, “On the Bicomplex $k$-Fibonacci Quaternions”, Communications in Advanced Mathematical Sciences, c. 2, sy. 3, ss. 227–234, 2019, doi: 10.33434/cams.542704.
ISNAD Torunbalcı Aydın, Fügen. “On the Bicomplex $k$-Fibonacci Quaternions”. Communications in Advanced Mathematical Sciences 2/3 (Eylül 2019), 227-234. https://doi.org/10.33434/cams.542704.
JAMA Torunbalcı Aydın F. On the Bicomplex $k$-Fibonacci Quaternions. Communications in Advanced Mathematical Sciences. 2019;2:227–234.
MLA Torunbalcı Aydın, Fügen. “On the Bicomplex $k$-Fibonacci Quaternions”. Communications in Advanced Mathematical Sciences, c. 2, sy. 3, 2019, ss. 227-34, doi:10.33434/cams.542704.
Vancouver Torunbalcı Aydın F. On the Bicomplex $k$-Fibonacci Quaternions. Communications in Advanced Mathematical Sciences. 2019;2(3):227-34.

Cited By

Unrestricted Fibonacci and Lucas quaternions
Fundamental Journal of Mathematics and Applications
https://doi.org/10.33401/fujma.752758
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