Exponential Riordan Arrays and Jacobi elliptic functions

Abstract

This paper establishes relationships between elliptic functions and Riordan arrays leading to new classes of Riordan arrays which here are called elliptic Riordan arrays. In particular, the case of Riordan arrays derived from Jacobi elliptic functions which are parameterized by the elliptic modulus k will be treated here. Some concrete examples of such Riordan arrays are presented via a recursive formula. Furthermore, some applications of these Riordan arrays corresponding to the solutions of the PDE modelling nonlinear wave phenomena for shallow water waves and nonlinear electric line transmission are highlighted.