Abstract
Özdemir defined the hybrid numbers as a generalization of complex, hyperbolic and dual numbers. In this research, we define the generalized Lucas hybrinomials with two variables. Also, we get the Binet formula, generating function and some properties for the generalized Lucas hybrinomials. Moreover, Catalan's, Cassini's and d'Ocagne's identities for these hybrinomials are obtained. Lastly, by the help of the matrix theory we derive the matrix representation of the generalized Lucas hybrinomials.
Highlights
Many researchers have studied on applications of the Fibonacci and the Lucas numbers for a long time in engineering, arts, physics and nature
These sequences have taken a huge interest of many authors
Bergum and Hoggatt studied on the generalized Lucas polynomials and de...ned these polynomials recursively by
Summary
Many researchers have studied on applications of the Fibonacci and the Lucas numbers for a long time in engineering, arts, physics and nature. We de...ne the generalized Lucas hybrinomials with two variables. We get the Binet formula, generating function and some properties for the generalized Lucas hybrinomials. Fibonacci numbers, Lucas numbers, polynomials, hybrinomials, recurrence relation.
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