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Tessarine Number Sequences and Quantum Calculus Approach

Cilt: 30 Sayı: 1 29 Nisan 2025
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Tessarine Number Sequences and Quantum Calculus Approach

Öz

This paper presents a detailed study of a new generation of tessarine number sequences with components including quantum integers Also, several fundamental identities are defined such as Binet formulas, Catalan, Cassini, D’ocagnes. After that, the q-Fibonacci tessarine and q-Lucas tessarine polynomials and function sequences are definedand obtained several properties for these sequences.

Anahtar Kelimeler

q-Fibonacci tessarine number sequences, q-Lucas tessarine number sequences, Tessarine numbers

Kaynakça

  1. Babadağ, F. (2017). Tessarines and homothetic exponential motions in 4-dimensional Euclidean space. Beykent University Journal of Science and Engineering, 10(1), 1-13.
  2. Babadağ, F., & Uslu, M. (2021). A new approach to Fibonacci tessarines with Fibonacci and Lucas number. Adıyaman University Journal of Science (ADYU J SCI), 11(2), 263-275. https://doi.org/10.37094/adyujsci.852037
  3. Babadağ, F. (2023). Quantum calculus approach to the dual number sequences. Research on Mathematics and Science- III, 3, 49-60. https://doi.org/10.58830/ozgur.pub252
  4. Cockle, J. (1849). III. On a new imaginary in algebra. The London Edinburgh and Dublin Philosophical Magazine and Journal of Science, 34(226), 37-47. https://doi.org/10.1080/14786444908646169
  5. Cockle, J. (1850). XXXI. On impossible equations, on impossible quantities, and on tessarines. The London Edinburgh and Dublin Philosophical Magazine and Journal of Science, 37(250), 281-283. https://doi.org/10.1080/14786445008646598
  6. Horadam, A. F. (1961). A generalized Fibonacci sequence. The American Mathematical Monthly, 68(5), 455-459. https://doi.org/10.1080/00029890.1961.11989696
  7. Horadam, A. F. (1963). Complex Fibonacci numbers and Fibonacci quaternions. The American Mathematical Monthly, 70(3), 289-291. https://doi.org/10.2307/2313129
  8. Kac, V., & Cheung, P. (2002). Quantum calculus. Springer. http://dx.doi.org/10.1007/978-1-4613-0071-7
  9. Kome, S., Kome, C., & Catarino, P. (2022). Quantum calculus approach to the dual bicomplex Fibonacci and Lucas number. Journal of Mathematical Extension, 6(2), 1-17. https://doi.org/10.30495/JME.2022.1906
  10. Koshy, T. (2018). Fibonacci and Lucas numbers with applications, 1. John Wiley Sons.

Kaynak Göster

APA
Babadağ, F. (2025). Tessarine Number Sequences and Quantum Calculus Approach. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 30(1), 92-101. https://doi.org/10.53433/yyufbed.1595620
AMA
1.Babadağ F. Tessarine Number Sequences and Quantum Calculus Approach. YYUFBED. 2025;30(1):92-101. doi:10.53433/yyufbed.1595620
Chicago
Babadağ, Faik. 2025. “Tessarine Number Sequences and Quantum Calculus Approach”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 30 (1): 92-101. https://doi.org/10.53433/yyufbed.1595620.
EndNote
Babadağ F (01 Nisan 2025) Tessarine Number Sequences and Quantum Calculus Approach. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 30 1 92–101.
IEEE
[1]F. Babadağ, “Tessarine Number Sequences and Quantum Calculus Approach”, YYUFBED, c. 30, sy 1, ss. 92–101, Nis. 2025, doi: 10.53433/yyufbed.1595620.
ISNAD
Babadağ, Faik. “Tessarine Number Sequences and Quantum Calculus Approach”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 30/1 (01 Nisan 2025): 92-101. https://doi.org/10.53433/yyufbed.1595620.
JAMA
1.Babadağ F. Tessarine Number Sequences and Quantum Calculus Approach. YYUFBED. 2025;30:92–101.
MLA
Babadağ, Faik. “Tessarine Number Sequences and Quantum Calculus Approach”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 30, sy 1, Nisan 2025, ss. 92-101, doi:10.53433/yyufbed.1595620.
Vancouver
1.Faik Babadağ. Tessarine Number Sequences and Quantum Calculus Approach. YYUFBED. 01 Nisan 2025;30(1):92-101. doi:10.53433/yyufbed.1595620