Titlebook: Complex Analysis; In the Spirit of Lip Rubí E. Rodríguez,Irwin Kra,Jane P. Gilman Textbook 2013Latest edition Springer Science+Business Med

expeditious

https://doi.org/10.1007/978-3-642-00342-4ize all simply connected domains in the extended complex plane. The first two sections of this chapter study the action of a quotient of the group of two-by-two nonsingular complex matrices on the extended complex plane, namely, the group PSL(2, .) and the projective special linear group. This group

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https://doi.org/10.1007/978-3-658-22569-8 own names. These are, of course, functions that arise naturally and repeatedly in various mathematical settings. Many of these functions are defined by infinite products. Examples of such . functions include Euler’s Γ-function, the Riemann ζ-function, and the Euler Φ-function. We will study only th

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The Cauchy Theory: Key Consequences,e chapter is very short, it includes proofs of many of the implications of the fundamental theorem in complex function theory (Theorem?1.1). We point out that these relatively compact proofs of a host of major theorems result from the work put into Chap.?4 and earlier chapters.

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Tremor

Anja Wildemann,Lena Bien-Miller theory of holomorphic functions, a role beyond enabling the construction of complex transcendental functions that are the extension of the real transcendental functions. A much stronger result holds. All holomorphic functions are (at least locally) convergent power series. This will be proven in the next chapter.