Here is a simple example of an expression I'd like to transform from a product of Bessel functions to a sum of a preferably finite number of Bessel functions:
$$J_0(u)J_1(v)$$
Since there are product-to-sum rules for cosine and sine, and since $J_0$ and $J_1$ have a somewhat similar relationship as that of cosine and sine via taking the derivative, I was curious. Based on some simple plots, I know that directly analogizing the cosine-sine rules is not valid.
Edit: I found and skimmed Bevilacqua et al but couldn't see any way to use their identities against the expression above. Lerche-Newberger and other results seem to only apply when the arguments to the two Bessel functions are the same.
