Titlebook: Complex Analysis; Taras Mel‘nyk Textbook 2023 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature

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Laurent Series: Isolated Singularities of Analytic Functions,ger .. These series were introduced by the French mathematician Pierre Laurent (1813–1854) in 1843. Laurent series are a valuable tool for studying the behavior of analytic functions near their isolated singularities, a classification of which is given here. It is noteworthy that, knowing the behavi

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Residue Calculus, singularities. In this chapter, we will illustrate this claim with examples of integral calculations. It turns out that in order to calculate the integral of an analytic function along a curve, it is necessary to determine some values, called ., of that function at its singularities. The reader can

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Analytic Continuations,nalytic functions, namely the possibility of continuing an analytic function from the domain in which it is defined to a larger one. An important property of the analytic continuation procedure is that it is unique. In essence, this means that knowing the values of an analytic function in a small do

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Textbook 2023, the Lagrange–Bürmann formula, and Puiseux series..Drawing from several decades of teaching experience, this book is ideally suited for one or two semester courses in complex analysis. It also serves as a valuable companion for courses in topology, approximation theory, asymptotic analysis, and fun

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https://doi.org/10.57088/978-3-7329-9013-9at are responsible for its zeros. The theory also supplies a ready-made framework for counting zeros and poles of a given meromorphic function or zeros of an analytic function, in particular, we prove the argument principle and Rouché’s theorem.

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Sprachen — Zuordnung — Strukturenlued function, and under which conditions the newly extended function is single-valued. Along the way we will be introduced to various continuation techniques and other fundamental concepts of complex analysis such as monodromy, global analytic functions, their singularities and Riemann surfaces.

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heorem, the Lagrange–Bürmann formula, and Puiseux series..Drawing from several decades of teaching experience, this book is ideally suited for one or two semester courses in complex analysis. It also serves as a valuable companion for courses in topology, approximation theory, asymptotic analysis, and fun978-3-031-39617-5978-3-031-39615-1