I want to solve for the asymptotic solution of the following differential equation
$$ \left(y^2+1\right) R''(y)+y\left(2-p \left(b_{0} \sqrt{y^2+1}\right)^{-p}\right) R'(y)-l (l+1) R(y)=0$$
as $y\rightarrow \infty$, where $p>0$. I did the standard way by obtaining a series solution by the Frobenius method prescription in the form
$$R(y)=\sum_{n=0}^\infty \frac{a_{n}}{y^{n+k}}$$ where $k=l+1$ is the indicial exponent. I had difficulty finding, by hand, for a recurrence relation for the coefficients $a_n$ for arbitrary value of the parameter $p$. Right now, I am just doing the brute force method of solving individual $a_n$ for every value of $p$.
But I am just wondering whether the recurrence relation is possible to obtain using Mathematica routine. Any help is appreciated.