I may have misread the question, but it seems to me like something known but non-trivial. That is to say, I think I know the answer, and in the discrete case I do know the answer, but only because this is a calculation I've seen in a few papers. On the other hand, rereading the OP's comment, it is not clear if the question I am thinking of is the question he or she is thinking of.
Anyway, would be interested to hear other people's thoughts on this one.
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