Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable |
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Page 97
... surface . It is not our intention to give , in this connection , a rigorous definition of this notion . For our purposes it is sufficient to introduce Riemann surfaces ... Riemann ANALYTIC FUNCTIONS AS MAPPINGS 97 Elementary Riemann Surfaces.
... surface . It is not our intention to give , in this connection , a rigorous definition of this notion . For our purposes it is sufficient to introduce Riemann surfaces ... Riemann ANALYTIC FUNCTIONS AS MAPPINGS 97 Elementary Riemann Surfaces.
Page 98
... Riemann surface . For this reason we must attach the lower edge of the first sheet to the upper edge of the second ... Riemann surface whose points are in one - to - one corre- spondence with the points of the z - plane . What is more ...
... Riemann surface . For this reason we must attach the lower edge of the first sheet to the upper edge of the second ... Riemann surface whose points are in one - to - one corre- spondence with the points of the z - plane . What is more ...
Page 278
... Riemann surfaces of elementary multiple - valued functions we introduce a set F ( the Riemann surface ) whose elements ( the points ) are the branches ( f , z ) of f . We are then in a position to consider f as a single - valued ...
... Riemann surfaces of elementary multiple - valued functions we introduce a set F ( the Riemann surface ) whose elements ( the points ) are the branches ( f , z ) of f . We are then in a position to consider f as a single - valued ...
Contents
COMPLEX NUMBERS | 1 |
2 | 17 |
Elementary Theory of Power Series | 33 |
Copyright | |
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a₁ algebraic analytic continuations analytic function angle arbitrary boundary bounded C₁ Cauchy's theorem Chap choose circle closed curve coefficients compact set complex numbers conclude condition conformal mapping consider constant contains convergence corresponding defined definition denote derivative determined differential disk end points equal equation exists finite number follows formula function elements function f(z ƒ dz geometric harmonic function hence homotopic imaginary inequality infinite initial branch interval inverse lemma limit line integral line segment linear transformation meromorphic meromorphic function metric space multiple neighborhood notation obtain open sets poles polygon polynomial positive proof prove radius real axis rectangle Riemann sphere Riemann surface satisfies sequence simple simply connected single-valued singularity subset Suppose symmetric tion topological totally bounded u₁ uniform convergence vanishes w-plane w₁ whole plane ди მყ