ABSTRACT
So far we have learned two ways of finding a series solution to a differential equation. If x0 is an ordinary point, we can find a Taylor series solution to the differential equation that will converge with a positive radius of convergence. If we have a regular singular point at x0, we can still use the Frobenius method to find the solutions expressed as series with a slightly different term. There is one case that we have yet to explore, and that is the behavior of a solution to a differential equation at an irregular singular point. If we consider the point at ∞, this is in fact the most common case that occurs.
