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Triple gaussian integral
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I think this should actually have the sum over c first, otherwise it seems to evaluate to zero
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I don't have any pen and paper with me, so I can't check it to be 100% correct right now...  But you might be able rewrite the exponential functions into delta-functions, and then make use of the sample property to make most of the integral cancel out, assuming that the delta symbolsisn't already a delta function
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You can change variables y->y-c and x->x-c, that way the integral over c separates from the others and can be done directly. For the x and y variables, diagonalize the quadratic form to have two seprable gaussians integrals.
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This is a question better suited for stack exchange.  Pretty sure no here has above a 12th grade education
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Have you tried wolfram alpha?

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