Irregular singularity

Summary

An irregular singularity of a linear differential equation is a singular point that is not a regular singular point. Near it, solutions can grow or decay faster than any power, typically like $e^{c / (z - z_0)^k}$ or $e^{c z^k}$ near $\infty$. The Frobenius method fails there, and the solutions are described by asymptotic expansions valid only in sectors. This leads to the Stokes phenomenon. See the definition.