Schwarz Reflection Principle
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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 pa...
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.
