Özdemir defined the hybrid numbers as a generalization of complex, hyperbolic and dual numbers. In this research, we define generalized Lucas hybrinomials with two variables. Also, get Binet formula, generating function some properties for hybrinomials. Moreover, Catalan's, Cassini's d'Ocagne's identities these are obtained. Lastly, by help matrix theory derive representation

Generalized nonnegative polynomials are defined as products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. In this paper we extend quadrature sums involving pth powers of polynomials to those for generalized polynomials.

In this study, we gave a generalization on Pell and Pell-Lucas octonions over the algebra $\mathbb{O}(a,b,c)$ where $a,b$ $c$ are real numbers. For these number sequences, obtain Binet formulas some well-known identities such as Catalan's identity, Cassini's identity d'Ocagne's identity.

Using basic identities, Lucas proved Theorem 0 in the first of his two 1878 articles in which he developed the general theory of second-order linear recurrences [5]; Lucas had previously proven parts (i) and (iii) in his 1875 article [4], Nearly four decades later, Carmichael [1] used the theory of cyclotomic polynomials to obtain both new results and results confirming and generalizing many of...