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

English
2026-03-17
€133.57 €166.96

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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 ... Full description

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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.

More Information

Publisher OmniScriptum
Release year 2026
Cover type Softcover
EAN 9786131164361
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€133.57 €166.96