Hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers

Abstract

Hybrid numbers which are accepted as a generalization of complex, hyperbolic and dual numbers, have attracted the attention of many researchers recently. In this paper, hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers are defined. Then some algebraic and combinatoric properties of these hybrinomials are examined such as the recurrence relations, summation formulas and generation functions. Additionally, hybrid hyper-Fibonacci and hybrid hyper-Lucas numbers are defined by using the hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers.