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

Year 2022, Volume: 40 Issue: 1, 179 - 187, 25.03.2022

Nurten Gürses , Gülsüm Yeliz Şentürk Salim Yüce

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

References

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