How to Evaluate a Complicated Sum
Does somebody know how to calculate the sum
$ \sum_{k=-\infty}^\infty \frac{1}{1+k^2} ? \ $
Wolfram said answer is π * coth(π). is there any easier way to do that? Yimin. Jan 20
Discussion/help
Big hint: See page 189 of the classic book, "Complex Analysis," by Lars Ahlfors and think about letting z=i in formula (11). After that, it will be like falling off a log ... head first.--Steve Bell 12:32, 21 January 2011 (UTC)
