A comprehensive survey of dual-generalized complex Fibonacci and Lucas numbers

Nurten Gürses; Gülsüm Yeliz Şentürk; Salim Yüce

EN

A comprehensive survey of dual-generalized complex Fibonacci and Lucas numbers

Abstract

This paper aims to develop dual-generalized complex Fibonacci and Lucas numbers and obtain recurrence relations. Fibonacci and Lucas’s approach to dual-generalized complex numbers contains dual-complex, hyper-dual and dual-hyperbolic situations as special cases and allows general contributions to the literature for all real number . For this purpose, Binet’s formulas along with Tagiuri’s, Hornsberger’s, D’Ocagne’s, Cassini’s and Catalan’s identities, are calculated for dual-generalized complex Fibonacci and Lucas numbers. Finally, the results are given, and the special cases for this unification are classified.

Keywords

References

The article references can be accessed from the .pdf file.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Nurten Gürses ^*
0000-0001-8407-854X
Türkiye

Gülsüm Yeliz Şentürk This is me
0000-0002-8647-1801
Türkiye

Salim Yüce This is me
0000-0002-8296-6495
Türkiye

Publication Date

March 25, 2022

Submission Date

March 26, 2021

Acceptance Date

July 5, 2021

Published in Issue

Year 2022 Volume: 40 Number: 1

IZ

https://izlik.org/JA47JZ95LX

Cite

RIS / Bibtex

APA

Gürses, N., Şentürk, G. Y., & Yüce, S. (2022). A comprehensive survey of dual-generalized complex Fibonacci and Lucas numbers. Sigma Journal of Engineering and Natural Sciences, 40(1), 179-187. https://izlik.org/JA47JZ95LX

AMA

1.Gürses N, Şentürk GY, Yüce S. A comprehensive survey of dual-generalized complex Fibonacci and Lucas numbers. SIGMA. 2022;40(1):179-187. https://izlik.org/JA47JZ95LX

Chicago

Gürses, Nurten, Gülsüm Yeliz Şentürk, and Salim Yüce. 2022. “A Comprehensive Survey of Dual-Generalized Complex Fibonacci and Lucas Numbers”. Sigma Journal of Engineering and Natural Sciences 40 (1): 179-87. https://izlik.org/JA47JZ95LX.

EndNote

Gürses N, Şentürk GY, Yüce S (March 1, 2022) A comprehensive survey of dual-generalized complex Fibonacci and Lucas numbers. Sigma Journal of Engineering and Natural Sciences 40 1 179–187.

IEEE

[1]N. Gürses, G. Y. Şentürk, and S. Yüce, “A comprehensive survey of dual-generalized complex Fibonacci and Lucas numbers”, SIGMA, vol. 40, no. 1, pp. 179–187, Mar. 2022, [Online]. Available: https://izlik.org/JA47JZ95LX

ISNAD

Gürses, Nurten - Şentürk, Gülsüm Yeliz - Yüce, Salim. “A Comprehensive Survey of Dual-Generalized Complex Fibonacci and Lucas Numbers”. Sigma Journal of Engineering and Natural Sciences 40/1 (March 1, 2022): 179-187. https://izlik.org/JA47JZ95LX.

JAMA

1.Gürses N, Şentürk GY, Yüce S. A comprehensive survey of dual-generalized complex Fibonacci and Lucas numbers. SIGMA. 2022;40:179–187.

MLA

Gürses, Nurten, et al. “A Comprehensive Survey of Dual-Generalized Complex Fibonacci and Lucas Numbers”. Sigma Journal of Engineering and Natural Sciences, vol. 40, no. 1, Mar. 2022, pp. 179-87, https://izlik.org/JA47JZ95LX.

Vancouver

1.Nurten Gürses, Gülsüm Yeliz Şentürk, Salim Yüce. A comprehensive survey of dual-generalized complex Fibonacci and Lucas numbers. SIGMA [Internet]. 2022 Mar. 1;40(1):179-87. Available from: https://izlik.org/JA47JZ95LX