1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: The identity theroem complex analysis

  1. Apr 1, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that there is no holomorphic function f in the open unit disk such that f(1/n)=((-1)^n)/(n^2) for n=2,3,4....

    2. Relevant equations
    The identity theorem: Let f and g be holomorphic functions in the connected open subset of C, G. If f(z)=g(z) for all z in a subset of G that has a limit point in G, then f=g.

    3. The attempt at a solution

    We proved in an earlier example that there is not holomorphic function f in the open unit disk such that f(1/n)=2^(-n) n=2,3,4... Is the above function identical to this? I thought this was the route to go but i am not sure anymore. I know we have to somehow use the identity theorem.
  2. jcsd
  3. Apr 1, 2008 #2
    Maybe it helps to consider the function [itex]g(z)=(-1)^{\frac{1}{z}}z^2[/itex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for identity theroem complex Date
Diff eq with constants.. Eulers identity.. Mar 17, 2018
Integration of even powers of sine and cosine Nov 7, 2017
Gamma Function Identities Sep 14, 2017
Theroem of closed sets containing limit Sep 25, 2013