Titlebook: Complex Analysis in One Variable; Raghavan Narasimhan,Yves Nievergelt Textbook 2001Latest edition Birkhäuser Boston 2001 Meromorphic funct

积习难改

https://doi.org/10.1007/978-1-4842-1239-4The following exercises provide some practice with manifolds that arise frequently in mathematics. The exercises for Chapter 9 contain other examples amenable to the methods from Chapter 2.

可用

https://doi.org/10.1007/978-1-4302-2498-3. Prove that for each compact subset . ⊂ ℂ the complement ℂ . has exactly one unbounded connected component.

放大

opalescence

Thymus

Picard’s TheoremIn this chapter, we shall prove the so-called “big” theorem of Picard which asserts that a holomorphic function with an (isolated) essential singularity assumes every value with at most one exception in any neighborhood of that singularity.

convert

Applications of Runge’s TheoremThis chapter is devoted to various theorems which can be proved using Runge’s theorem: the existence of functions with prescribed zeros or poles, a “cohomological” version of Cauchy’s theorem, and related theorems. The last section concerns itself with .(Ω) as a ring (or ℂ-algebra).

exorbitant

echnic

Anecdote

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