On recursive hyperbolic functions in Fibonacci-Lucas sense

Abstract

The hyperbolic Fibonacci and hyperbolic Lucas functions have been introduced before and have been improved to functions of the symmetrical form. In this paper, we generalize the mentioned definitions, which will be called Horadam hyperbolic sine function $ left( HSF right) $ and Horadam hyperbolic cosine function $ left( HCF right) $.Further, we present many identities and hyperbolic properties of our new definitions.