Question: Series of Bessel functions

I'm having trouble evaluating an expression with an infinite sum of bessel functions. The expression is:

or, in mathematical notation:

The program doesn't seem to be able to solve the expression and return a value. I only get the answer

When I try to evaluate a simple infinite sum like 

the answer is a value. Breaking up the expression in components and evaluating each one works in some cases, e.g. the expression 

which returns a value. However, the expression

fails, and returns

Is there a trick to evaluating infinite sums with indices appearing inside a function in the summation expression? Or am I doing something wrong?

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