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- Schwarz_reflection_principle abstract "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, the putative extension of F to the rest of the complex plane isorThat 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 a continuous function on the closed upper half plane , holomorphic on the upper half plane , which takes real values on the real axis. Then the extension formula given above is an analytic continuation to the whole complex plane.In practice it would be better to have a theorem that allows F certain singularities, for example F a meromorphic function. To understand such extensions, one needs a proof method that can be tweaked. In fact Morera's theorem is well adapted to proving such statements. Contour integrals involving the extension of F clearly split into two, using part of the real axis. So, given that the principle is rather easy to prove in the special case from Morera's theorem, understanding the proof is enough to generate other results.The principle also adapts to apply to harmonic functions.".
- Schwarz_reflection_principle wikiPageID "3213223".
- Schwarz_reflection_principle wikiPageRevisionID "556205920".
- Schwarz_reflection_principle hasPhotoCollection Schwarz_reflection_principle.
- Schwarz_reflection_principle id "p/r081990".
- Schwarz_reflection_principle title "Riemann-Schwarz principle".
- Schwarz_reflection_principle subject Category:Complex_analysis.
- Schwarz_reflection_principle subject Category:Harmonic_functions.
- Schwarz_reflection_principle subject Category:Mathematical_principles.
- Schwarz_reflection_principle subject Category:Theorems_in_complex_analysis.
- Schwarz_reflection_principle type Abstraction100002137.
- Schwarz_reflection_principle type Cognition100023271.
- Schwarz_reflection_principle type Communication100033020.
- Schwarz_reflection_principle type Content105809192.
- Schwarz_reflection_principle type Function113783816.
- Schwarz_reflection_principle type Generalization105913275.
- Schwarz_reflection_principle type HarmonicFunctions.
- Schwarz_reflection_principle type Idea105833840.
- Schwarz_reflection_principle type MathematicalPrinciples.
- Schwarz_reflection_principle type MathematicalRelation113783581.
- Schwarz_reflection_principle type Message106598915.
- Schwarz_reflection_principle type Principle105913538.
- Schwarz_reflection_principle type Proposition106750804.
- Schwarz_reflection_principle type PsychologicalFeature100023100.
- Schwarz_reflection_principle type Relation100031921.
- Schwarz_reflection_principle type Statement106722453.
- Schwarz_reflection_principle type Theorem106752293.
- Schwarz_reflection_principle type TheoremsInComplexAnalysis.
- Schwarz_reflection_principle comment "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, the putative extension of F to the rest of the complex plane isorThat is, we make the definition that agrees along the real axis.The result proved by H. A. Schwarz is as follows.".
- Schwarz_reflection_principle label "Schwarz reflection principle".
- Schwarz_reflection_principle label "Schwarzsches Spiegelungsprinzip".
- Schwarz_reflection_principle label "Принцип симметрии Шварца".
- Schwarz_reflection_principle sameAs Schwarzsches_Spiegelungsprinzip.
- Schwarz_reflection_principle sameAs 반사_원리.
- Schwarz_reflection_principle sameAs m.08zq73.
- Schwarz_reflection_principle sameAs Q4378892.
- Schwarz_reflection_principle sameAs Q4378892.
- Schwarz_reflection_principle sameAs Schwarz_reflection_principle.
- Schwarz_reflection_principle wasDerivedFrom Schwarz_reflection_principle?oldid=556205920.
- Schwarz_reflection_principle isPrimaryTopicOf Schwarz_reflection_principle.