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

 
9786131164361: Schwarz Reflection Principle: Mathematics, Analytic Function, Complex Variable, Complex Conjugate, Real Axis, Real Number

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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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