This is problem 13.3 from Rudin's Real and Complex analysis. It is not homework.(adsbygoogle = window.adsbygoogle || []).push({});

Is there a sequence of polynomials {Pn} such that Pn(0) = 1 for n = 1,2,3,... but Pn(z) -> 0 for all z != 0 as n -> infinity?

My guess here is no. Sketch of proof: Assume such a sequence existed. Then we should be able to contradict the maximum modulus theorem for any disk around 0 since all Pn(z) for |z| = r will be approaching 0 for large enough n, but Pn(0) = 1.

Is this correct?

thanks

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# Sequence of complex polynomials

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