## Analytic Function Theory, Volume 2 |

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absolutely convergent algebraic elements algebraic function analytic continuation analytic function asserted boundary bounded branch points coefficients compact subset completes the proof consider constant continuous function corresponding countable curve defined definition denote determine domain elliptic function entire function exists finite number finite plane Fn(z follows formula function f(z given gives Hence holds holomorphic function implies inequality infinite infinity integral interior interval Lemma limit point line segment meromorphic function neighborhood normal obtain period parallelogram poles polygon polynomial positive integers power series problem properties prove radius of convergence rational function real axis regular elements result right member roots satisfies Section sequence shows simply-connected single-valued singular point solution Suppose tends to zero that/(z Theorem theory Tn(z transformation uniform convergence uniformly with respect unique unit circle unit disk upper half-plane values Verify