Analytic Functions

a₁ absolutely convergent analytic element analytic function annular neighbourhood annulus arbitrary point assumes the value belong boundary called centre Chapter circle K circle K 0;1 circumference closed circle closed set coefficients complex numbers condition Consequently constant containing the point continuous function convex defined denumerable derivative elliptic function entire function entire open plane equal equation exercise exists expansion finite number following theorem formula func function F(z function holomorphic G₁ half-line half-plane hence holomorphic function holomorphic in G homographic inequality infinite integral interior lemma Let us denote logarithm meromorphic function multiple necessary and sufficient obtain open set G P₁ poles polynomial positive number power series Proof prove radius radius of convergence real axis real number region G respect right side roots satisfies segment set F single-valued subharmonic tends tion uniformly convergent uniquely invertible vanishes variable zero Σπί