- #1
Grothard
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Homework Statement
Compare the function f(z) = (pi/sin(pi*z))^2 to the summation of g(z) = 1/(z-n)^2 for n ranging from negative infinity to infinity. Show that their difference is
1) pole-free, i.e. analytic
2) of period 1
3) bounded in the strip 0 < x < 1
Conclude that they are equivalent
The Attempt at a Solution
Part 2 is easy to show; I don't need any help with that one.
I'm working on part 1 right now. I noticed that in both equations there exist poles whenever z is an integer, and those are the only poles. This means that the two functions have exactly the same poles. I'm not sure how to use that to prove that their difference has no poles, though.