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

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Sigma Mühendislik ve Fen Bilimleri Dergisi
Volume:40 Issue:1
A comprehensive survey of dual-generalized complex Fibonacci and Lucas numbers

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

Authors : Nurten GÜRSES, Gülsüm Yeliz ŞENTÜRK, Salim YÜCE

Pages : 179-187

View : 34 | Download : 6

Publication Date : 2022-03-25

Article Type : Research Paper

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 : Dual generalized complex numbers, Fibonacci numbers, Lucas numbers, MSC 2010, 11B39, 11B83

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