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q-Leonardo Bicomplex Numbers

Yıl 2023, Cilt: 11 Sayı: 2, 176 - 183, 31.10.2023

Fügen Torunbalcı Aydın

Öz

Abstract: In the paper, we define the $q$-Leonardo bicomplex numbers by using the $q$-integers. Also, we give some algebraic properties of $q$-Leonardo bicomplex numbers such as recurrence relation, generating function, Binet's formula, D'Ocagne's identity, Cassini's identity, Catalan's identity and Honsberger identity.

Anahtar Kelimeler

Bicomplex number q-integer Fibonacci number Bicomplex Fibonacci number Leonardo number q-Leonardo number q-Leonardo bicomplex number

Kaynakça

  • [1] Adler S. L., and others. Quaternionic quantum mechanics and quantum fields, Oxford University Press on Demand, 88, (1995).
  • [2] Y. Alp and E.G. Koc¸er, Some properties of Leonardo numbers., Konuralp Journal of Mathematics (KJM), 9(1), (2021), 183-189.
  • [3] I. Akkus, G. Kizilaslan, Quaternions: Quantum calculus approach with applications., Kuwait Journal of Science, 46 (4), (2019).
  • [4] Andrews G. E., Askey R., and Roy R. Special functions, Cambridge University Press, 71, (1999).
  • [5] Arfken G. B., and Weber H. J. Mathematical methods for physicists, American Association of Physics Teachers, (1999).
  • [6] F. Torunbalcı Aydın, Bicomplex fibonacci quaternions., Chaos Solitons Fractals, Vol. 106, (2018), 147-153.
  • [7] F. Torunbalcı Aydın, q-Fibonacci bicomplex and q-Lucas bicomplex numbers., Notes on Number Theory and Discrete Mathematics, 28(2),(2022), 261-275.
  • [8] M. Turan, S. O¨ zkaldı Karakus¸ and S. Nurkan, A New Perspective on Bicomplex Numbers: Leonardo Component Extension., preprint, (2022).
  • [9] P. Catarino, and Anabela Borges, On leonardo numbers., Acta Mathematica Universitatis Comenianae, 89(1), (2019), 75-76.
  • [10] P. Catarino and A. Borges, A note on incomplete Leonardo numbers., Integers, Vol. 20(7), (2020).
  • [11] S. Halıcı, On bicomplex Fibonacci numbers and their generalization., Models and Theories in Social Systems, (2019), 509-524.
  • [12] Kac V. G., and Cheung P. Quantum calculus, Springer 113, (2002).
  • [13] C. Kızılates¸, A new generalization of Fibonacci hybrid and Lucas hybrid numbers., Chaos, Solitons and Fractals, 130, 109449, (2020).
  • [14] M. Luna-Elizarraras, M. Shapiro, D. C. Struppa, A. Vajiac, Bicomplex numbers and their elementary functions., Cubo (Temuco) 14 (2), (2012), 61-80.
  • [15] M. Luna-Elizarraras, M. Shapiro, D. C. Struppa, A. Vajiac, Bicomplex holomorphic functions: the algebra, geometry and analysis of bicomplex numbers., Birkhauser, (2015)
  • [16] S. Kaya Nurkan and A. I. G¨uven, A note on bicomplex Fibonacci and Lucas numbers., arXiv preprint arXiv:1508.03972, (2015).
  • [17] D. Rochon and M. Shapiro, On algebraic properties of bicomplex and hyperbolic numbers., Anal. Univ. Oradea, fasc. math, 11, (71), (2004), 110.
  • [18] Segre C. Le rappresentazioni reali delle forme complesse e gli ente iper-algebrici, Mathematische Annalen, Vol. 40(3), 413-467 (1892).
  • [19] A. G. Shannon, A note on generalized Leonardo numbers., Notes on Number Theory and Discrete Mathematics, 25(3), (2019), 97-101.
  • [20] R. P. M. Vieira, F. R. V. Alves, and P. M. M. C. Catarino, Relac¸ ˜oes bidimensionais e identidades da sequˆencia de Leonardo., Revista Sergipana de Matem´atica e Educac¸ ˜ao Matem´atica, 4(2), (2019), 156-173 .

Yıl 2023, Cilt: 11 Sayı: 2, 176 - 183, 31.10.2023

Fügen Torunbalcı Aydın

Öz

Kaynakça

  • [1] Adler S. L., and others. Quaternionic quantum mechanics and quantum fields, Oxford University Press on Demand, 88, (1995).
  • [2] Y. Alp and E.G. Koc¸er, Some properties of Leonardo numbers., Konuralp Journal of Mathematics (KJM), 9(1), (2021), 183-189.
  • [3] I. Akkus, G. Kizilaslan, Quaternions: Quantum calculus approach with applications., Kuwait Journal of Science, 46 (4), (2019).
  • [4] Andrews G. E., Askey R., and Roy R. Special functions, Cambridge University Press, 71, (1999).
  • [5] Arfken G. B., and Weber H. J. Mathematical methods for physicists, American Association of Physics Teachers, (1999).
  • [6] F. Torunbalcı Aydın, Bicomplex fibonacci quaternions., Chaos Solitons Fractals, Vol. 106, (2018), 147-153.
  • [7] F. Torunbalcı Aydın, q-Fibonacci bicomplex and q-Lucas bicomplex numbers., Notes on Number Theory and Discrete Mathematics, 28(2),(2022), 261-275.
  • [8] M. Turan, S. O¨ zkaldı Karakus¸ and S. Nurkan, A New Perspective on Bicomplex Numbers: Leonardo Component Extension., preprint, (2022).
  • [9] P. Catarino, and Anabela Borges, On leonardo numbers., Acta Mathematica Universitatis Comenianae, 89(1), (2019), 75-76.
  • [10] P. Catarino and A. Borges, A note on incomplete Leonardo numbers., Integers, Vol. 20(7), (2020).
  • [11] S. Halıcı, On bicomplex Fibonacci numbers and their generalization., Models and Theories in Social Systems, (2019), 509-524.
  • [12] Kac V. G., and Cheung P. Quantum calculus, Springer 113, (2002).
  • [13] C. Kızılates¸, A new generalization of Fibonacci hybrid and Lucas hybrid numbers., Chaos, Solitons and Fractals, 130, 109449, (2020).
  • [14] M. Luna-Elizarraras, M. Shapiro, D. C. Struppa, A. Vajiac, Bicomplex numbers and their elementary functions., Cubo (Temuco) 14 (2), (2012), 61-80.
  • [15] M. Luna-Elizarraras, M. Shapiro, D. C. Struppa, A. Vajiac, Bicomplex holomorphic functions: the algebra, geometry and analysis of bicomplex numbers., Birkhauser, (2015)
  • [16] S. Kaya Nurkan and A. I. G¨uven, A note on bicomplex Fibonacci and Lucas numbers., arXiv preprint arXiv:1508.03972, (2015).
  • [17] D. Rochon and M. Shapiro, On algebraic properties of bicomplex and hyperbolic numbers., Anal. Univ. Oradea, fasc. math, 11, (71), (2004), 110.
  • [18] Segre C. Le rappresentazioni reali delle forme complesse e gli ente iper-algebrici, Mathematische Annalen, Vol. 40(3), 413-467 (1892).
  • [19] A. G. Shannon, A note on generalized Leonardo numbers., Notes on Number Theory and Discrete Mathematics, 25(3), (2019), 97-101.
  • [20] R. P. M. Vieira, F. R. V. Alves, and P. M. M. C. Catarino, Relac¸ ˜oes bidimensionais e identidades da sequˆencia de Leonardo., Revista Sergipana de Matem´atica e Educac¸ ˜ao Matem´atica, 4(2), (2019), 156-173 .
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Articles
Yazarlar

Fügen Torunbalcı Aydın 0000-0001-9292-1832

Yayımlanma Tarihi 31 Ekim 2023
Gönderilme Tarihi 14 Mart 2023
Kabul Tarihi 31 Mayıs 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 11 Sayı: 2

Kaynak Göster

APA Torunbalcı Aydın, F. (2023). q-Leonardo Bicomplex Numbers. Konuralp Journal of Mathematics, 11(2), 176-183.
AMA Torunbalcı Aydın F. q-Leonardo Bicomplex Numbers. Konuralp J. Math. Ekim 2023;11(2):176-183.
Chicago Torunbalcı Aydın, Fügen. “Q-Leonardo Bicomplex Numbers”. Konuralp Journal of Mathematics 11, sy. 2 (Ekim 2023): 176-83.
EndNote Torunbalcı Aydın F (01 Ekim 2023) q-Leonardo Bicomplex Numbers. Konuralp Journal of Mathematics 11 2 176–183.
IEEE F. Torunbalcı Aydın, “q-Leonardo Bicomplex Numbers”, Konuralp J. Math., c. 11, sy. 2, ss. 176–183, 2023.
ISNAD Torunbalcı Aydın, Fügen. “Q-Leonardo Bicomplex Numbers”. Konuralp Journal of Mathematics 11/2 (Ekim 2023), 176-183.
JAMA Torunbalcı Aydın F. q-Leonardo Bicomplex Numbers. Konuralp J. Math. 2023;11:176–183.
MLA Torunbalcı Aydın, Fügen. “Q-Leonardo Bicomplex Numbers”. Konuralp Journal of Mathematics, c. 11, sy. 2, 2023, ss. 176-83.
Vancouver Torunbalcı Aydın F. q-Leonardo Bicomplex Numbers. Konuralp J. Math. 2023;11(2):176-83.
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