Given a power series $\sum_{n=0}^{\infty} a_nx^n$ satisfies:
$$\ a_{n+2}+ ( n^2 -\alpha^2 )a_n = 0 $$
For all $\ n\geq 2 $
Assume $\ \alpha $ is an integer.
What is the radius of convergence ofthe power series?
I tried using the ratio test to calculate the radius of convergence but I am stuck on the very first step. Any help or hints will be very much appreciated!