Titlebook: Complex Analysis, Riemann Surfaces and Integrable Systems; Sergey M. Natanzon Textbook 2019 Springer Nature Switzerland AG 2019 meromorphi

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,Vitexin β-glucosyltransferase,In what follows, we use the binomial coefficients . given by . for . ≥ . ≥ 0 and . otherwise, with the standard convention that 0! = 1.

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Meromorphic Functions,Now we turn to studying the properties of functions holomorphic in non-simply connected domains.

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Riemann Mapping Theorem,A family . of functions is said to be . .if for every compact set . ⊂ . there exists a constant . = .(.) such that |.(.)|≤ . for all ., . ∈ ..

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Harmonic Functions,As before, we identify the real plane . with the complex plane . setting . = . + .. Recall that an open connected subset . is called a ..

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Riemann Surfaces and Their Modules,A . is a one-dimensional complex manifold. A Riemann surface is defined as an equivalence class of atlases of charts on a surface with biholomorphic transition maps.