Complex Analysis | Part IB, 2005

State the Cauchy integral formula, and use it to deduce Liouville's theorem.

Let ff be a meromorphic function on the complex plane such that f(z)/zn\left|f(z) / z^{n}\right| is bounded outside some disc (for some fixed integer nn ). By considering Laurent expansions, or otherwise, show that ff is a rational function in zz.

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