# differential equations – Resolution of the recurrence relation for the expansion coefficients of the asymptotic expansion of an ODE

I want to solve the asymptotic solution of the following differential equation

$$left (y ^ 2 + 1 right) R & # 39; (y) + y left (2 -p left (b_ {0} sqrt {y ^ 2 + 1} right) ^ {- p} right) R (## EQU1 ## + 1) R (y) = 0$$

as $$y rightarrow infty$$, or $$p> 0$$. I used the standard method in obtaining a serial solution according to the Frobenius method, in the form

$$R (y) = sum_ {n = 0} ^ infty frac {a_ {n}} {y ^ {n + k}}$$
or $$k = l + 1$$ is the indicative exponent. I had trouble finding, by hand, a recurrence relation for the coefficients $$a_n$$ for arbitrary value of the parameter $$p$$. Right now, I'm only doing the brute force method of individual resolution $$a_n$$ for each value of $$p$$.

But I'm just wondering if the recurrence relation is possible to use with the Mathematica routine. Any help is appreciated.