A Study on Dual Hyperbolic Fibonacci and Lucas Numbers

Abstract

In this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers. Additionally, we give the identities regarding negadual-hyperbolic Fibonacci and negadual-hyperbolic Lucas numbers. Finally, Binet formulas, D’Ocagne, Catalan and Cassini identities are obtained for dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers.

Keywords

• dual-hyperbolic numbers
• dual-hyperbolic fibonacci numbers
• dual-hyperbolic lucas numbers
• primary 11b39
• secondary 11b83