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## Main Question or Discussion Point

I posted the same question on Math Stackexchange: http://math.stackexchange.com/questions/1084724/calculating-harmonic-sums-with-residues/1085248#1085248

The answer there using complex analysis is great. I had questions, which Id like to get advice on here.

The answer there using complex analysis is great. I had questions, which Id like to get advice on here.

**(1)**How did he get the laurent series at negative integers? I can never understand how that works. Doesnt he need to find the coefficient a_n? Which is defined as a contour integral? How does the Laurent series work for digamma?**(2)**How did he get the partial sum involving the q−1 in the upper index? And finally, I dont understand the step from: "which yields.. this implies that.." How did he make the transformation? It didnt change anything?