Hello. This is the most closely matching forum I found for this, so I hope my question fits here. I was looking at the following proof of the Central-Limit theorem: http://physics.ucsc.edu/~peter/250/deriv_climit.pdf and after Eq. (10) it says: "Expanding out the exponential in the last expression and comparing powers of k one finds that the first few cumulants are..." but I don't see how the equalities in the next lines stem from it. Could someone please explicitly show that? Thanks.