ISSN: 1304-7191 | E-ISSN: 1304-7205
A comprehensive survey of dual-generalized complex Fibonacci and Lucas numbers
1Department of Mathematics, Faculty of Arts and Sciences, Yıldız Technical University, Istanbul, Turkey
2Department of Computer Engineering, Faculty of Engineering and Architecture, Istanbul Gelisim University, Istanbul, Turkey
Sigma J Eng Nat Sci 2022; 40(1): 179-187 DOI: 10.14744/sigma.2022.00014
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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 p. 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.