Question

Triple gaussian integral

Answer 1

I think this should actually have the sum over c first, otherwise it seems to evaluate to zero

Answer 2

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

Answer 3

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.

Answer 4

This is a question better suited for stack exchange.  Pretty sure no here has above a 12th grade education

Answer 5

Have you tried wolfram alpha?