Jacobi Theta Functions are a set of special functions that arise in various areas of mathematics, particularly in the study of elliptic functions and complex analysis. They are defined using infinite series and are closely related to the theory of modular forms. These functions are typically denoted as θ₁, θ₂, θ₃, and θ₄, each having distinct properties and applications. These functions play a crucial role in number theory, combinatorics, and mathematical physics. They are used to solve problems involving partitions, lattice points, and even in the study of string theory. The Jacobi Theta Functions also have connections to elliptic curves, making them significant in both pure and applied mathematics.