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 {F-k,F-n}(n=0)(infinity), recently found by studying the recursive application of two geometrical transformations onto (C) over bar = C boolean OR {+infinity} 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. (C) 2006 Elsevier Ltd. All rights reserved.