# Exponential Riordan Arrays and Jacobi elliptic functions

## TL;DR

This paper introduces elliptic Riordan arrays derived from Jacobi elliptic functions, establishing new mathematical relationships and providing recursive formulas and examples for these arrays.

## Contribution

It develops a novel class of Riordan arrays based on elliptic functions, expanding the mathematical framework and applications of Riordan arrays.

## Key findings

- New elliptic Riordan arrays linked to Jacobi elliptic functions
- Recursive formulas for specific elliptic Riordan arrays
- Concrete examples illustrating the properties of these arrays

## 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 that are parameterized by the elliptic modulus $k$ will be treated here. Some concrete examples of such Riordan arrays are presented via a recursive formula.