14.8 Prove that, for each d > 0, the series o n=1 n-z converges uniformly on...

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14.8 Prove that, for each d > 0, the series o n=1 n-z converges uniformly on {z : Rez >1+6}. Deduce that the series defines a holomorphic function ((2) in {z Rez > 1}. (This is the Riemann zeta function, of great interest in number theory. It is discussed briefly in the Appendix.) 14.8 Prove that, for each d > 0, the series o n=1 n-z converges uniformly on {z : Rez >1+6}. Deduce that the series defines a holomorphic function ((2) in {z Rez > 1}. (This is the Riemann zeta function, of great interest in number theory. It is discussed briefly in the Appendix.)

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To prove that the series on converges uniformly on z Rez 1 6 we can use the Weierstrass Mtest Let fn... View the full answer