Calculating Harmonic Sums using Residues

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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.

(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?
 

Answers and Replies

  • #2
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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