Hyperbolic functions obtained from k-Jacobsthal sequences

Abstract

In this paper, an expansion of the classical hyperbolic functions is presented and studied. Also, many features of the [Formula: see text]-Jacobsthal hyperbolic functions are given. Finally, we introduced some graph and curved surfaces related to the [Formula: see text]-Jacobsthal hyperbolic functions.

On hyperbolic k-Jacobsthal and k-Jacobsthal–Lucas octonions

“…Many generalizations of number sequences were then described and studied [4,5,12,15,19]. One of these generalizations is the Jacobsthal numbers [7,8,14,15,17,19]. The Jacobsthal numbers 𝐽 𝑛 are defined by the relation 𝐽 𝑛+2 = 𝐽 𝑛+1 + 2𝐽 𝑛 , 𝑛 ≥ 0 with 𝐽 0 = 0 and 𝐽 1 = 1.…”