Hyperbolic Horadam hybrid functions

Abstract

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.