thats a nice one, you hit me under the belt lol...i need to upgrade my memory lolI overlooked that one. Does it say there that you are usibg the Frobenius method to solve the Bessel equation ? (other link , link, solution with pictures, a whole chapter, ...).
And you should really start your power series from ##k=0##, not from ##k=-\infty##.
All this with just a little googling and without sitting down and seriously working out your core question ! Lazy me ...
My own notes are still somewhere in the attic and also in my brain, but under four and a half decades of dust