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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?