The problem is to prove the following:
\sum_{m>0}J_{j+m}(x)J_{j+m+n}(x) = \frac{x}{2n}\left(J_{j+1}(x)J_{j+n}(x) - J_{j}(x)J_{j+n+1}(x)\right).
Now for the rambling...
I've been reading for a while, but this is my first post. Did a quick search, but I didn't find anything relevant. I could...