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The representation of one region on another
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2-plane absolute value analytic curve analytic function angle assume axes boundary points branch point centre circumference coincide Complete complex number complex values complex variable conformal representation conjugate considered const constants continuous convergence convex polygon corre corresponding point critical point curves Demy differential domain E. V. Lucas Eiemann surface ellipse equation Fcap finite follows function f(z given circle H. A. Schwarz half plane hyperbola Illustrated infinite number infinitesimal inside the circle integral interior point intersect linear substitution linear transformation moves negative neighbourhood obtained origin orthogonal parabola point z0 positive half quarter plane real axis reciprocal radii rectangle region regular represented rotation Second Edition sides simply connected simply connected surfaces singular point slit sphere spond stereographic projection straight lines system of circles theorem tion trans transformation by means triangle uniquely unit circle upper sheet zero