The k-Fibonacci hyperbolic functions

An extension of the classical hyperbolic functions is introduced and studied. These new k-Fibonacci hyperbolic functions generalize also the k  -Fibonacci sequences, say {Fk,n}n=0∞, recently found by studying the recursive application of two geometrical transformations onto C¯=C∪{+∞} used in the well-known four-triangle longest-edge (4TLE) partition. In this paper, several properties of these k-Fibonacci hyperbolic functions are studied in an easy way. We finalize with the introduction of some curves and surfaces naturally related with the k-Fibonacci hyperbolic functions.