Dual-Gaussian Pell and Pell-Lucas numbers

Hasan Gökbaş

doi:10.17776/csj.1067983

EN

Dual-Gaussian Pell and Pell-Lucas numbers

Abstract

In this study, we define a new type of Pell and Pell-Lucas numbers which are called dual-Gaussian Pell and dual-Gaussian Pell-Lucas numbers. We also give the relationship between negadual-Gaussian Pell and Pell-Lucas numbers and dual-complex Pell and Pell-Lucas numbers. Also, some sum ve product properties of Pell and Pell-Lucas numbers are given. Moreover, we obtain the Binet’s formula, generating function, d’Ocagne’s identity, Catalan’s identity, Cassini’s identity and some sum formulas for these new type numbers. Some algebraic proporties of dual-Gaussian Pell and Pell-Lucas numbers are investigated. Futhermore, we give the matrix representation of dual-Gaussian Pell and Pell-Lucas numbers.

Keywords

References

[1] Horadam A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, American Math. Monthly, 70 (1963) 289-291.
[2] Fjelstad P., Gal S.G., n-dimensional Dual Complex Numbers, Advances in Applied Clifford Algebras, 8(2) (1998) 309-322.
[3] Clifford W.K., A Preliminary Sketch of Biquaternions, (1873).
[4] Messelmi F., Dual Complex Numbers and Their Holomorphic Functions, https://hal.archives-ouvertes.fr/hal-01114178. Retrieved January 7, 2022.
[5] Catarino P., Bicomplex k-Pell Quaternions, Computational Methods and Function Theory, 19 (2019) 65-76.
[6] Gül K., Dual Bicomplex Horadam Quaternions, Notes on Numbers Theory and Discrete Mathematics, 26 (2020) 187-205.
[7] Soykan S., On Dual Hyperbolic Generalized Fibonacci Numbers, Indian Journal of Pure and Applied Mathematics, 52 (2021) 62-78.
[8] Vajda S., Fibonacci and Lucas Numbers and the Golden Section, Ellis Horwood Limited Publ., England, (1989).

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Hasan Gökbaş ^*
0000-0002-3323-8205
Türkiye

Publication Date

December 27, 2022

Submission Date

February 3, 2022

Acceptance Date

October 2, 2022

Published in Issue

Year 2022 Volume: 43 Number: 4

DOI

https://doi.org/10.17776/csj.1067983

IZ

https://izlik.org/JA59DH73CH

Cite

RIS / Bibtex

APA

Gökbaş, H. (2022). Dual-Gaussian Pell and Pell-Lucas numbers. Cumhuriyet Science Journal, 43(4), 665-671. https://doi.org/10.17776/csj.1067983

AMA

1.Gökbaş H. Dual-Gaussian Pell and Pell-Lucas numbers. CSJ. 2022;43(4):665-671. doi:10.17776/csj.1067983

Chicago

Gökbaş, Hasan. 2022. “Dual-Gaussian Pell and Pell-Lucas Numbers”. Cumhuriyet Science Journal 43 (4): 665-71. https://doi.org/10.17776/csj.1067983.

EndNote

Gökbaş H (December 1, 2022) Dual-Gaussian Pell and Pell-Lucas numbers. Cumhuriyet Science Journal 43 4 665–671.

IEEE

[1]H. Gökbaş, “Dual-Gaussian Pell and Pell-Lucas numbers”, CSJ, vol. 43, no. 4, pp. 665–671, Dec. 2022, doi: 10.17776/csj.1067983.

ISNAD

Gökbaş, Hasan. “Dual-Gaussian Pell and Pell-Lucas Numbers”. Cumhuriyet Science Journal 43/4 (December 1, 2022): 665-671. https://doi.org/10.17776/csj.1067983.

JAMA

1.Gökbaş H. Dual-Gaussian Pell and Pell-Lucas numbers. CSJ. 2022;43:665–671.

MLA

Gökbaş, Hasan. “Dual-Gaussian Pell and Pell-Lucas Numbers”. Cumhuriyet Science Journal, vol. 43, no. 4, Dec. 2022, pp. 665-71, doi:10.17776/csj.1067983.

Vancouver

1.Hasan Gökbaş. Dual-Gaussian Pell and Pell-Lucas numbers. CSJ. 2022 Dec. 1;43(4):665-71. doi:10.17776/csj.1067983