Research Article
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Year 2026, Volume: 22 Issue: 1, 54 - 59, 30.03.2026
https://doi.org/10.18466/cbayarfbe.1669535
https://izlik.org/JA36GL43CN

Abstract

References

  • [1]. Cockle, J. 1848. On certain functions resembling quaternions and on a new imaginary in algebra. Philosophical Magazine and Journal of Science, London-Dublin-Edinburg; 3(33): 435-439.
  • [2]. Cockle, J. 1849. On a new imaginary in algebra. Philosophical Magazine and Journal of Science, London-Dublin-Edinburgh; 3(34): 37-47.
  • [3]. Cockle, J. 1849. On the symbols of algebra and on the theory of tessarines. Philosophical magazine and Journal of Science, London-Dublin-Edinburg; 3(34): 406-410.
  • [4]. Alp, Y, Koçer, EG. 2021. Some properties of Leonardo numbers. Konuralp Journal of Mathematics; 9(1): 183-189.
  • [5]. Catarino, P, Borges, A. 2019. On leonardo numbers. Acta Mathematica Universitatis Comenianae; 89(1): 75-86, 2019.
  • [6]. Kızılateş, C. 2020. A new generalization of Fibonacci hybrid and Lucas hybrid numbers. Chaos, Solitons and Fractals; 130: 109449.
  • [7]. Catarino, P, Borges, A. 2020. A Note On Incomplete Leonardo Numbers. Integers: Electronic Journal of Combinatorial Number Theory; 20(7): 1-7.
  • [8]. Turan, M, Karakuş, SÖ, Nurkan, SK. 2023. A new perspective on bicomplex numbers with Leonardo number components. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics; 72(2): 340-351.
  • [9]. Babadağ, F, Atasoy, A. 2024. A new approach to Leonardo number sequences with the dual vector and dual angle representation. AIMS Mathematics; 9(6):14062-14074.
  • [10]. Babadağ, F, Uslu, M. 2021. A New Approach to Fibonacci Tessarines with Fibonacci and Lucas Number Components. Adıyaman University Journal of Science; 11(2): 263-275.
  • [11]. Kac, VG., Cheung, P. Quantum calculus, Springer, 113, 2002.
  • [12]. Adler, SL. Quaternionic quantum mechanics and quantum fields, Oxford University Press on Demand, 88, 1995.
  • [13]. Andrews, GE, Askey, R, Roy, R. Special functions, Cambridge University Press, 71, 1999.
  • [14]. Aydın, FT. 2023. q-Leonardo Bicomplex Numbers. Konuralp Journal of Mathematics; 11(2): 176-183.
  • [15]. Akkuş, İ, Kızılaslan, G. 2019. Quaternions: Quantum calculus approach with applications. Kuwait Journal of Science; 46(4): 1-13.
  • [16]. Karataş, A. 2023. Dual Leonardo numbers. AIMS Mathematics; 8(12): 30527-30536.
  • [17]. Shannon, AG. 2019. A note on generalized Leonardo numbers. Notes on Number Theory and Discrete Mathematics; 25(3): 97-101.
  • [18]. Aydın, FT. 2022. q-Fibonacci bicomplex and q-Lucas bicomplex numbers. Notes on Number Theory and Discrete Mathematics; 28(2): 261-275.
  • [19]. Aydın, FT. 2018. Bicomplex fibonacci quaternions. Chaos Solitons Fractals; 106: 147-153.
  • [20]. Babadağ, F. 2017. A new approach to homothetic motions and surfaces with tessarines. International Journal of New Technology and Research; 3: 45-48.
  • [21]. Beites, PD, Catarino, P. 2024. On the Leonardo quaternions sequence. Hacettepe Journal of Mathematics and Statistics; 53(4): 1001-1023.
  • [22]. Moreira, C, França, P, Beites, PD. 2023. Uma fórmula de tipo Binet para os números de Geonardo. Gazeta de Matemática; 201: 20-23.
  • [23]. Fonseca, CM da, Kızılateş, C, Saraiva, P, Shannon, AG. 2025. Generalised Leonardo numbers. Logic Journal of the IGPL; jzaf005. https://doi.org/10.1093/jigpal/jzaf005
  • [24]. Shannon, AG, Horadam, AF. 1972. Some Properties of Third-Order Recurrence Relations. The Fibonacci Quarterly; 10(2): 135-146. https://doi.org/10.1080/00150517.1972.12430952

Some Identities for q-Leonardo Tessarines

Year 2026, Volume: 22 Issue: 1, 54 - 59, 30.03.2026
https://doi.org/10.18466/cbayarfbe.1669535
https://izlik.org/JA36GL43CN

Abstract

In this paper, we introduce the concept of -Leonardo tessarines, which are defined using the q-integers. We then proceed to investigate the algebraic properties of these numbers, encompassing recurrence relations, generating functions, and several noteworthy identities. The study offers a thorough examination of the -Leonardo tessarines and their implications within algebraic frameworks.

References

  • [1]. Cockle, J. 1848. On certain functions resembling quaternions and on a new imaginary in algebra. Philosophical Magazine and Journal of Science, London-Dublin-Edinburg; 3(33): 435-439.
  • [2]. Cockle, J. 1849. On a new imaginary in algebra. Philosophical Magazine and Journal of Science, London-Dublin-Edinburgh; 3(34): 37-47.
  • [3]. Cockle, J. 1849. On the symbols of algebra and on the theory of tessarines. Philosophical magazine and Journal of Science, London-Dublin-Edinburg; 3(34): 406-410.
  • [4]. Alp, Y, Koçer, EG. 2021. Some properties of Leonardo numbers. Konuralp Journal of Mathematics; 9(1): 183-189.
  • [5]. Catarino, P, Borges, A. 2019. On leonardo numbers. Acta Mathematica Universitatis Comenianae; 89(1): 75-86, 2019.
  • [6]. Kızılateş, C. 2020. A new generalization of Fibonacci hybrid and Lucas hybrid numbers. Chaos, Solitons and Fractals; 130: 109449.
  • [7]. Catarino, P, Borges, A. 2020. A Note On Incomplete Leonardo Numbers. Integers: Electronic Journal of Combinatorial Number Theory; 20(7): 1-7.
  • [8]. Turan, M, Karakuş, SÖ, Nurkan, SK. 2023. A new perspective on bicomplex numbers with Leonardo number components. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics; 72(2): 340-351.
  • [9]. Babadağ, F, Atasoy, A. 2024. A new approach to Leonardo number sequences with the dual vector and dual angle representation. AIMS Mathematics; 9(6):14062-14074.
  • [10]. Babadağ, F, Uslu, M. 2021. A New Approach to Fibonacci Tessarines with Fibonacci and Lucas Number Components. Adıyaman University Journal of Science; 11(2): 263-275.
  • [11]. Kac, VG., Cheung, P. Quantum calculus, Springer, 113, 2002.
  • [12]. Adler, SL. Quaternionic quantum mechanics and quantum fields, Oxford University Press on Demand, 88, 1995.
  • [13]. Andrews, GE, Askey, R, Roy, R. Special functions, Cambridge University Press, 71, 1999.
  • [14]. Aydın, FT. 2023. q-Leonardo Bicomplex Numbers. Konuralp Journal of Mathematics; 11(2): 176-183.
  • [15]. Akkuş, İ, Kızılaslan, G. 2019. Quaternions: Quantum calculus approach with applications. Kuwait Journal of Science; 46(4): 1-13.
  • [16]. Karataş, A. 2023. Dual Leonardo numbers. AIMS Mathematics; 8(12): 30527-30536.
  • [17]. Shannon, AG. 2019. A note on generalized Leonardo numbers. Notes on Number Theory and Discrete Mathematics; 25(3): 97-101.
  • [18]. Aydın, FT. 2022. q-Fibonacci bicomplex and q-Lucas bicomplex numbers. Notes on Number Theory and Discrete Mathematics; 28(2): 261-275.
  • [19]. Aydın, FT. 2018. Bicomplex fibonacci quaternions. Chaos Solitons Fractals; 106: 147-153.
  • [20]. Babadağ, F. 2017. A new approach to homothetic motions and surfaces with tessarines. International Journal of New Technology and Research; 3: 45-48.
  • [21]. Beites, PD, Catarino, P. 2024. On the Leonardo quaternions sequence. Hacettepe Journal of Mathematics and Statistics; 53(4): 1001-1023.
  • [22]. Moreira, C, França, P, Beites, PD. 2023. Uma fórmula de tipo Binet para os números de Geonardo. Gazeta de Matemática; 201: 20-23.
  • [23]. Fonseca, CM da, Kızılateş, C, Saraiva, P, Shannon, AG. 2025. Generalised Leonardo numbers. Logic Journal of the IGPL; jzaf005. https://doi.org/10.1093/jigpal/jzaf005
  • [24]. Shannon, AG, Horadam, AF. 1972. Some Properties of Third-Order Recurrence Relations. The Fibonacci Quarterly; 10(2): 135-146. https://doi.org/10.1080/00150517.1972.12430952
There are 24 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory, Algebraic and Differential Geometry
Journal Section Research Article
Authors

Ali Atasoy 0000-0002-1894-7695

Submission Date April 3, 2025
Acceptance Date November 24, 2025
Publication Date March 30, 2026
DOI https://doi.org/10.18466/cbayarfbe.1669535
IZ https://izlik.org/JA36GL43CN
Published in Issue Year 2026 Volume: 22 Issue: 1

Cite

APA Atasoy, A. (2026). Some Identities for q-Leonardo Tessarines. Celal Bayar University Journal of Science, 22(1), 54-59. https://doi.org/10.18466/cbayarfbe.1669535
AMA 1.Atasoy A. Some Identities for q-Leonardo Tessarines. CBUJOS. 2026;22(1):54-59. doi:10.18466/cbayarfbe.1669535
Chicago Atasoy, Ali. 2026. “Some Identities for Q-Leonardo Tessarines”. Celal Bayar University Journal of Science 22 (1): 54-59. https://doi.org/10.18466/cbayarfbe.1669535.
EndNote Atasoy A (March 1, 2026) Some Identities for q-Leonardo Tessarines. Celal Bayar University Journal of Science 22 1 54–59.
IEEE [1]A. Atasoy, “Some Identities for q-Leonardo Tessarines”, CBUJOS, vol. 22, no. 1, pp. 54–59, Mar. 2026, doi: 10.18466/cbayarfbe.1669535.
ISNAD Atasoy, Ali. “Some Identities for Q-Leonardo Tessarines”. Celal Bayar University Journal of Science 22/1 (March 1, 2026): 54-59. https://doi.org/10.18466/cbayarfbe.1669535.
JAMA 1.Atasoy A. Some Identities for q-Leonardo Tessarines. CBUJOS. 2026;22:54–59.
MLA Atasoy, Ali. “Some Identities for Q-Leonardo Tessarines”. Celal Bayar University Journal of Science, vol. 22, no. 1, Mar. 2026, pp. 54-59, doi:10.18466/cbayarfbe.1669535.
Vancouver 1.Ali Atasoy. Some Identities for q-Leonardo Tessarines. CBUJOS. 2026 Mar. 1;22(1):54-9. doi:10.18466/cbayarfbe.1669535