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The PoissonJensen Formula
The Characteristic Function
17 other sections not shown
bounded set characteristic function chordal distance circle constant convergence type convex function Corollary defined equality is possible equation f(z f(re finite number function f(z gives Hence hypothesis inequality Jensen's formula kn+1 left hand side lemma log f log f(z log+ l/r log+ M(r log+ T(R,f log+f mean type meromorphic function minimal type Note NQ(r number of roots number of zeros order and type Picard's theorem plane Poisson-Jensen formula pole of order poles of f(z polynomial proof of theorem proves the theorem q log+ rational rational function residue theorem Riemann sphere right hand side roots of f(z second fundamental theorem star-like suitable sequence Suppose f(z tends to infinity tends to zero theorem 13 theorem 9 unit circle univalent w-plane zeros and poles zeros of f(z zeros or poles