Jacobi-Anger expansion ($e^{\mathrm{i}z\sin \theta }={\sum }_{k\in \mathbb{Z}}{J}_k(z)e^{\mathrm{i}k\theta }$)

The Jacobi–Anger expansion is a mathematical identity that expresses the exponential function of a complex argument in terms of Bessel functions of the first kind. Specifically, it characterizes the relationship between the exponential function and the Bessel functions when the argument of the exponential function is a complex variable.