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Answer on Complex Analysis Question for toota

Question #16929
consider the series S(z)=(sum from n=1 to infinity) sin(z)/n^2 (1+cos(piz))
a) prove that this series does not converge uniformly on C.
Expert's answer
S(z)=(sum from n=1 to infinity) sin(z)/n^2 (1+cos(piz))
|Fn(x)-F(x)|<e->0
n-> sin(z)/n^w(1+cos(piz)), so at n=0 it goes to infinity.
That means, there is no uniform converging.

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