# Answer to Question #16929 in Complex Analysis 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.

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.

|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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