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Schwarz Reflection Principle: Mathematics, Analytic Function, Complex Variable, Complex Conjugate, Real Axis, Real Number -

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2026-03-17
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High Quality Content by WIKIPEDIA articles! In mathematics, the Schwarz reflection principle is a way to extend the domain of definition of an analytic function of a complex variable F, which is defined on the upper half-plane and has well-defined and real number boundary values on the real axis. In that case, writing * for complex conjugate, the putative extension of F to the rest of the complex plane is F ... Visas aprašymas

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High Quality Content by WIKIPEDIA articles! In mathematics, the Schwarz reflection principle is a way to extend the domain of definition of an analytic function of a complex variable F, which is defined on the upper half-plane and has well-defined and real number boundary values on the real axis. In that case, writing * for complex conjugate, the putative extension of F to the rest of the complex plane is F(z*)* or F(z*) = F*(z). That is, we make the definition that agrees along the real axis. The result proved by H. A. Schwarz is as follows. Suppose that F is holomorphic, for z with imaginary part > 0, and a real-valued continuous function on the real axis. Then the extension formula given above is an analytic continuation to the whole complex plane.

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Leidėjas OmniScriptum
Išleidimo metai 2026
Viršelio tipas Minkšti viršeliai
EAN 9786131164361
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125,22 € 166,96 €