Hybrid hyper-Fibonacci and hyper-Lucas numbers

Abstract

Different number systems have been studied lately. Recently, many researchers have considered the hybrid numbers which are generalization of the complex, hyperbolic and dual number systems. In this paper, we define the hybrid hyper-Fibonacci and hyper-Lucas numbers. Furthermore, we obtain some algebraic properties of these numbers such as the recurrence relations, the generating functions, the Binet’s formulas, the summation formulas, the Catalan’s identity, the Cassini’s identity and the d’Ocagne’s identity.