Hey everyone!

When finding a series solution for a certain ODE (at an ordinary point or a regular singular point), do we usually care about the radius of convergence or the lower bound of this radius?

Another thing. what's the lower bound of a solution at an ordinary point, say for the ODE $\displaystyle y''+2y'+y=0$ we know that $\displaystyle y_1=\sum_{n=0}^{\infty}\frac{x^n}{n!}$

Thanks?