@christianp This looks like a good candidate for induction/limit. I would move to partial sums, then pull the sum inside the product for what is here the denominator, and work out a formula in terms of the number of terms n in the partial sum, then take the limit of that formula as n increases.
@christianp *frowns* ok, the sum doesn't pull inside /directly/, but you get what i mean; it's only a five term expansion at worst. Definitely go from (inductively proved) finite sum formulas on the individual sub-functions of k.
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