Interesting. Reminds me of the “snake oil” technique useful when evaluating complex sums in combinatorics. By treating the sum in question as the coefficient of x^n in another sum, you can often obtain an expression where finding the coefficient of x^n — which is the value you’re after — is simple.
I think this is the same trick I eventually (too late) found to make my model tractable assuming a bivariate Normal. It certainly hadn't been my first instinct to consider rate of change with respect to correlation.
I wonder how many downvoters of this relevant XKCD reference actually read the article and understand that Feynman's Integral Trick involves differentiating under the integral sign. The relevant XKCD is about how much simpler it is to differentiate than to integrate (which can frequently be impossible using standard college calculus techniques).
