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tion I z 1 application of the principle of symmetry
Elementary transcendental functions the fundamental tran
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absolute convergence algebraic branch points analytic function angle boundary contours centre Chapter circles of Apollonius complex number complex potential conformal mapping construct continuous coordinate origin corresponding cosh curves defined determined domain bounded domain G doublet doubly connected domain ellipse equal equation equipotential lines essential singularity expansion exterior finite flow following assertions formula function f(z Green's function half-strip harmonic function harmonic measure Hint imaginary axis infinite number integral function limit point linear transformations logarithmic branch points maps the upper natural number neighbourhood parameters plane with cuts point at infinity point z0 polygon principal value Prove the following radius of convergence real axis real number rectangle respect Riemann surface segment semicircle sheets simple poles single-valued solution straight line stream lines strip symmetry principle theorem unit circle unit disk upper half-plane velocity vertices vortex source whole plane z-plane zero