Titlebook: Explorations in Complex Functions; Richard Beals,Roderick S. C. Wong Textbook 2020 Springer Nature Switzerland AG 2020 Complex analysis te

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Harmonic functions,ach harmonic. Conversely, at least locally, a real-valued harmonic function is the real part of a holomorphic function. A mean value property of these functions leads to analogues of the maximum modulus principle and its strong version.

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The Schwarzian derivative,ithmic derivative . of .. Here we show that the Schwarzian derivative is a natural object: a measure of the “curvature” of ., the pointwise deviation from a best approximation of . by a linear fractional transformation.

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Value distribution theory,s, counting multiplicity. Early in the development of complex function theory it was known that each rational function, as a function on the Riemann sphere, takes every value (finite or infinite) the same number of times.

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,Theorems of Phragmén–Lindelöf and Paley–Wiener,basic conclusion is that a function holomorphic on an unbounded domain ., and continuous on the closure, either grows very fast at infinity or is bounded by its values on the boundary of .. This has a number of interesting applications. Among them are a theorem of Hardy that characterizes the Gaussi

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0072-5285 warzian, the Riemann hypothesis, and parametrization of Riem.This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection o

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Pediatric and Adolescent Obesityart 1/2. Determining the truth of this assertion was one of the problems in Hilbert’s famous list of outstanding mathematical problems (1900). The problem is still open at the time of this writing. It has (often) been called the greatest unsolved problem of mathematics.

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