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Year 2020, Volume: 69 Issue: 2, 1104 - 1110, 31.12.2020

Gamaliel Cerda-morales

https://doi.org/10.31801/cfsuasmas.696617
https://izlik.org/JA23NR56JB

Abstract

References

  • Cerda-Morales, G., On generalized Fibonacci and Lucas numbers by matrix methods, Hacettepe journal of mathematics and statistics, 42(2) (2013), 173-179. Halici, S., On Fibonacci quaternions, Adv. Appl. Clifford Algebras, 22 (2012), 321-327. Halici, S., On complex Fibonacci quaternions, Adv. Appl. Clifford Algebras, 23 (2013), 105-112.
  • Halici, S., Karataş, A., On a generalization for Fibonacci quaternions, Chaos, Solitons and Fractals, 98 (2017), 178-182.
  • Horadam, A. F., Complex Fibonacci numbers and Fibonacci quaternions, Am. Math. Month., 70 (1963), 289-291.
  • Horadam, A. F., Quaternion recurrence relations, Ulam Quarterly, 2 (1993), 23-33 .
  • Horadam, A. F., Jacobsthal representation numbers, Fibonacci Quarterly, 34 (1996), 40-54.
  • Ipek, A., On (p,q)-Fibonacci quaternions and their Binet formulas, generating functions and certain binomial sums, Adv. Appl. Clifford Algebras, 27 (2017), 1343-1351.
  • Iyer, M. R., A note on Fibonacci quaternions, Fibonacci Quaterly, 7(3) (1969), 225-229.
  • Patel, B.K., Ray, P.K., On the properties of (p,q)-Fibonacci and (p,q)-Lucas quaternions, Mat. Rep. 21(1) (2019), 15-25.

Some identities involving (p,q)-Fibonacci and Lucas quaternions

Year 2020, Volume: 69 Issue: 2, 1104 - 1110, 31.12.2020

Gamaliel Cerda-morales

https://doi.org/10.31801/cfsuasmas.696617
https://izlik.org/JA23NR56JB

Abstract

In this study, we firstly examined the Horadam quaternions defined and studied by Halici and Karataş. Then, we used the Binet's formula to show some properties of the (p,q)-Fibonacci and Lucas quaternions. We also give some important identities including these quaternions. In this paper we have also contributed for the study of (p,q)-Fibonacci and Lucas quaternion sequence, deducing some of their identities using the Binet-style formula of Horadam quaternions. It is our intention to continue the study of this type of sequences, exploring some their applications in the science domain.

Keywords

Generalized Fibonacci quaternion Generalized Lucas Sequence Lucas Number

References

  • Cerda-Morales, G., On generalized Fibonacci and Lucas numbers by matrix methods, Hacettepe journal of mathematics and statistics, 42(2) (2013), 173-179. Halici, S., On Fibonacci quaternions, Adv. Appl. Clifford Algebras, 22 (2012), 321-327. Halici, S., On complex Fibonacci quaternions, Adv. Appl. Clifford Algebras, 23 (2013), 105-112.
  • Halici, S., Karataş, A., On a generalization for Fibonacci quaternions, Chaos, Solitons and Fractals, 98 (2017), 178-182.
  • Horadam, A. F., Complex Fibonacci numbers and Fibonacci quaternions, Am. Math. Month., 70 (1963), 289-291.
  • Horadam, A. F., Quaternion recurrence relations, Ulam Quarterly, 2 (1993), 23-33 .
  • Horadam, A. F., Jacobsthal representation numbers, Fibonacci Quarterly, 34 (1996), 40-54.
  • Ipek, A., On (p,q)-Fibonacci quaternions and their Binet formulas, generating functions and certain binomial sums, Adv. Appl. Clifford Algebras, 27 (2017), 1343-1351.
  • Iyer, M. R., A note on Fibonacci quaternions, Fibonacci Quaterly, 7(3) (1969), 225-229.
  • Patel, B.K., Ray, P.K., On the properties of (p,q)-Fibonacci and (p,q)-Lucas quaternions, Mat. Rep. 21(1) (2019), 15-25.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Gamaliel Cerda-morales 0000-0003-3164-4434

Submission Date March 1, 2020
Acceptance Date May 15, 2020
Publication Date December 31, 2020
DOI https://doi.org/10.31801/cfsuasmas.696617
IZ https://izlik.org/JA23NR56JB
Published in Issue Year 2020 Volume: 69 Issue: 2

Cite

APA Cerda-morales, G. (2020). Some identities involving (p,q)-Fibonacci and Lucas quaternions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1104-1110. https://doi.org/10.31801/cfsuasmas.696617
AMA 1.Cerda-morales G. Some identities involving (p,q)-Fibonacci and Lucas quaternions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1104-1110. doi:10.31801/cfsuasmas.696617
Chicago Cerda-morales, Gamaliel. 2020. “Some Identities Involving (p,q)-Fibonacci and Lucas Quaternions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 (2): 1104-10. https://doi.org/10.31801/cfsuasmas.696617.
EndNote Cerda-morales G (December 1, 2020) Some identities involving (p,q)-Fibonacci and Lucas quaternions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1104–1110.
IEEE [1]G. Cerda-morales, “Some identities involving (p,q)-Fibonacci and Lucas quaternions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1104–1110, Dec. 2020, doi: 10.31801/cfsuasmas.696617.
ISNAD Cerda-morales, Gamaliel. “Some Identities Involving (p,q)-Fibonacci and Lucas Quaternions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 1, 2020): 1104-1110. https://doi.org/10.31801/cfsuasmas.696617.
JAMA 1.Cerda-morales G. Some identities involving (p,q)-Fibonacci and Lucas quaternions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1104–1110.
MLA Cerda-morales, Gamaliel. “Some Identities Involving (p,q)-Fibonacci and Lucas Quaternions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, Dec. 2020, pp. 1104-10, doi:10.31801/cfsuasmas.696617.
Vancouver 1.Gamaliel Cerda-morales. Some identities involving (p,q)-Fibonacci and Lucas quaternions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020 Dec. 1;69(2):1104-10. doi:10.31801/cfsuasmas.696617

Cited By

Some results on Horadam quaternions
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Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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