Titlebook: Complex Analysis; Joseph Bak,Donald J. Newman Textbook 2010Latest edition Springer Science+Business Media, LLC 2010 Analysis.Complex analy

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Joseph Bak,Donald J. NewmanThe solution of the cubic equation and Newton‘s method for approximating the zeroes of any polynomial.Expanded treatments of the Schwarz reflection principle and of the mapping properties of analytic

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Analytic Continuation; The Gamma and Zeta Functions,f there exists a function ., analytic in .. and such that . = . throughout .. By the Uniqueness Theorem (6.9) any such continuation of . is uniquely determined. (It is possible, however, to have two analytic continuations .. and .. of a function . to regions .. and .. respectively with . throughout .. See Exercise 1.)

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Brenden J. Balcik,Aaron J. MonseauWe now show that if f is entire and if.then the Integral Theorem (4.15) and Closed Curve Theorem (4.16) apply to . as well as to .. (Note that since . is entire, . is continuous; however, it is not obvious that . is entire.)We begin by showing that the Rectangle Theorem applies to ..

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Katherine M. Edenfield,Jocelyn R. GravleeAs we have seen, it can happen that a function . is analytic on a closed curve . and yet ..

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Aufgabenstellung und Vorgehensweise,. While we have concentrated until now on the general properties of analytic functions, we now focus on the special behavior of an analytic function in the neighborhood of an “isolated singularity.”