I'm trying to solve a problem using the power series solution. Finally (and after substitution of differentations) I have come up with $$ -\frac1{2\mu}\sum_{i=2}^p i(i-1)a_i r^{(i-1)}+\frac1{2\mu}\omega \sum_{i=1}^p i\,a_i \,r^{(i+1)}-\frac{(l+1)}{\mu}\sum_{i=1}^p i\,a_i\,r^{(i-1)}-\frac{(4\mu^2-1)}{8\mu}\omega^2\sum_{i=0}^p a_i\,r^{(i+3)}+\frac{(2l+3)}{4\mu}\omega\sum_{i=0}^p a_i\,r^{i+1}-\sum_{i=0}^p a_i\,r^{i}=0 $$ According the power series solutions method now it's time to equalize the summation limits and powers of $r$, but here the powers include a variable called $l$. For this reason I'm confused how to proceed this calculation and get recursion relations?
Addendum: As a user said there is no need to include $l$'s in the summations. So I divided out them. Now the problem is equalizing the powers and limits.