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Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients

Year 2023, , 106 - 113, 30.09.2023
https://doi.org/10.32323/ujma.1339603

Abstract

In this paper, we introduce hybrid numbers with Fibonacci and Lucas hybrid number coefficients. We give the Binet formulas, generating functions, and exponential generating functions for these numbers. Then we define an associate matrix for these numbers. In addition, using this matrix, we present two different versions of Cassini identity of these numbers.

References

  • [1] M. Özdemir, Introduction to hybrid numbers, Adv. Appl. Clifford Algebras, 28(11) (2018).
  • [2] R. Nunes, Erlangen’s program for space-time through space-time geometric algebra induced by the R vector characteristic of the ring of hybrid numbers Z, (2021), arXiv:2106.11106 [physics.gen-ph].
  • [3] A. Petroianu, Bridging Circuits and Fields: Foundational Questions in Power Theory, CRC Press, 2021.
  • [4] A. Szynal-Liana, I. Wloch, The Fibonacci hybrid numbers, Util. Math., 110 (2019), 3–10.
  • [5] G. Cerda-Morales, Investigation of generalized hybrid Fibonacci numbers and their properties, Appl. Math. E-Notes, 21 (2021), 110–118.
  • [6] N. Irmak, More identities for Fibonacci and Lucas quaternions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(1) (2020), 369–375.
  • [7] C. Kızılateş, A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos, Solitons & Fractals, 130 (2020), 1–5.
  • [8] C. Kızılateş, A Note on Horadam hybrinomials, Fundam. J. Math. Appl., 5(1) (2022), 1–9.
  • [9] M. Liana, A. Szynal-Liana, I. Wloch, On Pell hybrinomials, Miskolc Math. Notes, 20(2) (2019), 1051–1062.
  • [10] A. Szynal-Liana, The Horadam hybrid numbers, Discussiones Mathematicae General Algebra and Applications, 38(1) (2018), 91–98.
  • [11] A. Szynal-Liana, I. Wloch, On Pell and Pell-Lucas hybrid number, Commentationes Math., 58 (2018), 11–17.
  • [12] A. Szynal-Liana, I. Wloch, On Jacobsthal and Jacobsthal-Lucas hybrid numbers, Ann. Math. Sil., 33 (2019), 276–283.
  • [13] A. Szynal-Liana, I. Wloch, Introduction to Fibonacci and Lucas hybrinomials, Complex Var. Elliptic Equ., 65 (2020), 1736–1747.
  • [14] A. Szynal-Liana, I. Wloch, On special spacelike hybrid numbers, Mathematics, 8(10) (2020), 1–10.
  • [15] A. Szynal-Liana, I. Wloch, Generalized Fibonacci-Pell hybrinomials, Online J. Anal. Comb., 15 (2020), 1–12.
  • [16] T. Şentürk, G. Bilgici, A. Daşdemir, Z. Ünal, A study on Horadam hybrid numbers, Turkish J. Math., 44 (2020), 1212–1221.
  • [17] E. Polatlı, A note on ratios of Fibonacci hybrid and Lucas hybrid numbers, Notes Number Theory Discrete Math., 27(3) (2021), 73–78.
  • [18] E. Karaca, F. Yılmaz, An introduction to harmonic complex numbers and harmonic hybrid Fibonacci numbers: A unified approach, Notes Number Theory Discrete Math., 28(3) (2022), 542–557.
  • [19] C. H. King, Some Properties of Fibonacci Numbers, Master’s Thesis, San Jose State College, 1960.
  • [20] I. D. Ruggles, VE Hoggatt, A primer on the Fibonacci sequences-Part IV, Fibonacci Q., 1(4) (1963), 65–71.
  • [21] E. Polatlı, Hybrid numbers with Fibonacci and Lucas hybrid number coefficients, (2020), Preprints 2020120349.
Year 2023, , 106 - 113, 30.09.2023
https://doi.org/10.32323/ujma.1339603

Abstract

References

  • [1] M. Özdemir, Introduction to hybrid numbers, Adv. Appl. Clifford Algebras, 28(11) (2018).
  • [2] R. Nunes, Erlangen’s program for space-time through space-time geometric algebra induced by the R vector characteristic of the ring of hybrid numbers Z, (2021), arXiv:2106.11106 [physics.gen-ph].
  • [3] A. Petroianu, Bridging Circuits and Fields: Foundational Questions in Power Theory, CRC Press, 2021.
  • [4] A. Szynal-Liana, I. Wloch, The Fibonacci hybrid numbers, Util. Math., 110 (2019), 3–10.
  • [5] G. Cerda-Morales, Investigation of generalized hybrid Fibonacci numbers and their properties, Appl. Math. E-Notes, 21 (2021), 110–118.
  • [6] N. Irmak, More identities for Fibonacci and Lucas quaternions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(1) (2020), 369–375.
  • [7] C. Kızılateş, A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos, Solitons & Fractals, 130 (2020), 1–5.
  • [8] C. Kızılateş, A Note on Horadam hybrinomials, Fundam. J. Math. Appl., 5(1) (2022), 1–9.
  • [9] M. Liana, A. Szynal-Liana, I. Wloch, On Pell hybrinomials, Miskolc Math. Notes, 20(2) (2019), 1051–1062.
  • [10] A. Szynal-Liana, The Horadam hybrid numbers, Discussiones Mathematicae General Algebra and Applications, 38(1) (2018), 91–98.
  • [11] A. Szynal-Liana, I. Wloch, On Pell and Pell-Lucas hybrid number, Commentationes Math., 58 (2018), 11–17.
  • [12] A. Szynal-Liana, I. Wloch, On Jacobsthal and Jacobsthal-Lucas hybrid numbers, Ann. Math. Sil., 33 (2019), 276–283.
  • [13] A. Szynal-Liana, I. Wloch, Introduction to Fibonacci and Lucas hybrinomials, Complex Var. Elliptic Equ., 65 (2020), 1736–1747.
  • [14] A. Szynal-Liana, I. Wloch, On special spacelike hybrid numbers, Mathematics, 8(10) (2020), 1–10.
  • [15] A. Szynal-Liana, I. Wloch, Generalized Fibonacci-Pell hybrinomials, Online J. Anal. Comb., 15 (2020), 1–12.
  • [16] T. Şentürk, G. Bilgici, A. Daşdemir, Z. Ünal, A study on Horadam hybrid numbers, Turkish J. Math., 44 (2020), 1212–1221.
  • [17] E. Polatlı, A note on ratios of Fibonacci hybrid and Lucas hybrid numbers, Notes Number Theory Discrete Math., 27(3) (2021), 73–78.
  • [18] E. Karaca, F. Yılmaz, An introduction to harmonic complex numbers and harmonic hybrid Fibonacci numbers: A unified approach, Notes Number Theory Discrete Math., 28(3) (2022), 542–557.
  • [19] C. H. King, Some Properties of Fibonacci Numbers, Master’s Thesis, San Jose State College, 1960.
  • [20] I. D. Ruggles, VE Hoggatt, A primer on the Fibonacci sequences-Part IV, Fibonacci Q., 1(4) (1963), 65–71.
  • [21] E. Polatlı, Hybrid numbers with Fibonacci and Lucas hybrid number coefficients, (2020), Preprints 2020120349.
There are 21 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Articles
Authors

Emrah Polatlı 0000-0002-2349-8978

Early Pub Date September 18, 2023
Publication Date September 30, 2023
Submission Date August 8, 2023
Acceptance Date September 17, 2023
Published in Issue Year 2023

Cite

APA Polatlı, E. (2023). Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients. Universal Journal of Mathematics and Applications, 6(3), 106-113. https://doi.org/10.32323/ujma.1339603
AMA Polatlı E. Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients. Univ. J. Math. Appl. September 2023;6(3):106-113. doi:10.32323/ujma.1339603
Chicago Polatlı, Emrah. “Hybrid Numbers With Fibonacci and Lucas Hybrid Number Coefficients”. Universal Journal of Mathematics and Applications 6, no. 3 (September 2023): 106-13. https://doi.org/10.32323/ujma.1339603.
EndNote Polatlı E (September 1, 2023) Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients. Universal Journal of Mathematics and Applications 6 3 106–113.
IEEE E. Polatlı, “Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients”, Univ. J. Math. Appl., vol. 6, no. 3, pp. 106–113, 2023, doi: 10.32323/ujma.1339603.
ISNAD Polatlı, Emrah. “Hybrid Numbers With Fibonacci and Lucas Hybrid Number Coefficients”. Universal Journal of Mathematics and Applications 6/3 (September 2023), 106-113. https://doi.org/10.32323/ujma.1339603.
JAMA Polatlı E. Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients. Univ. J. Math. Appl. 2023;6:106–113.
MLA Polatlı, Emrah. “Hybrid Numbers With Fibonacci and Lucas Hybrid Number Coefficients”. Universal Journal of Mathematics and Applications, vol. 6, no. 3, 2023, pp. 106-13, doi:10.32323/ujma.1339603.
Vancouver Polatlı E. Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients. Univ. J. Math. Appl. 2023;6(3):106-13.

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