 Jacobi elliptic functions

Jacobi elliptic functions are a set of basic elliptic functions that generalize trigonometric functions and are used in many areas of mathematics, including number theory, algebraic geometry, and physics. They are particularly useful in the study of elliptic curves and in solving problems involving periodic phenomena. The Jacobi elliptic functions are defined in terms of a parameter, typically denoted as \(k\) (or \(m\)), which is called the elliptic modulus.