The aim of this paper is to define hyper-Leonardo hybrinomials as a generalization of the Leonardo Pisano hybrinomials and to examine some of their properties such as the recurrence relation, summation formula and generating function. Another aim is to introduce hyper hybrid-Leonardo numbers.

In this paper, we first introduce a new generalization of Frank matrix which is a lower Hessenberg matrix. Then, we examine its algebraic structure, determinant, inverse, LU decomposition and characteristic polynomial.

The aim of this paper is to introduce the hybrid form of the hyperbolic Horadam function and to investigate some of its properties such as the generating function. Another aim is to define hyperbolic Horadam hybrid sine and cosine functions and their symmetrical forms. For newly defined functions, some properties such as the recursive relations, derivatives, Cassini and De Moivre type identities are examined. In addition, the quasi-sine Horadam hybrid function and three-dimensional Horadam hybrid spiral are defined.

In this paper, hyper-Fibonacci and hyper-Lucas polynomials are defined and some of their algebraic and combinatorial properties such as the recurrence relations, summation formulas, and generating functions are presented. In addition, some relationships between the hyper-Fibonacci and hyper-Lucas polynomials are given.

The aim of this paper is to define hyper-Leonardo hybrinomials as a generalization of the Leonardo Pisano hybrinomials and to examine some of their properties such as the recurrence relation, summation formula and generating function. Another aim is to introduce hyper-Leonardo hybrid numbers.