# Series solutions near an irregular singularity

1. Mar 24, 2013

### ShayanJ

Consider a linear differential equation of the form $y''+p(x)y'+q(x)y=0$ with an irregular singularity at $x_0$.
How can I found a series solution to it near $x_0$?

Thanks

2. Mar 24, 2013

### HallsofIvy

Staff Emeritus
Basic answer- you don't, there isn't one. If your differential equation has an "irregular singularity" at x0, then there is no series solution in a neighborhood of x0.

3. Mar 24, 2013

### ShayanJ

Can you explain why?

Thanks