Just a sort of general question, but when solving Bessel DE's, for example for only integer values of n, do you usually just leave them in the form of $$y(x) = AJ_n(x)+B Y_n(x)$$ or do you actually simplify the answers/put them in the form of summations? If you'd have to do the second option, for, let's say order $0$, or order $1$, how would one compute the limits in the $Y_n(x)$ part?
I'm really sorry if this seems like a dumb question btw, it's just that everywhere I look, I only see the solutions in the form of the equation that I wrote above, but no expansion/simplification anywhere.
Edit: removed an incorrect assumption that $Y_0=0$.