Rolf Nevanlinna creator V Paatero creator Rolf Nevanlinna text xxu Providence, Rhode Island : AMS Chelsea Pub./American Mathematical Society ;2007 2nd ed. monographic eng

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ix, 350 pages : illustrations ; 26 cm The authors present topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem The concept of an analytic function General properties of rational functions Linear transformations Mapping by rational functions of second order The exponential function and its inverse. The general power The trigonometric functions Infinite series with complex terms Integration in the complex domain. Cauchy's theorem Cauchy's integral formula and its applications The residue theorem and its applications Harmonic functions Analytic continuation Entire functions Periodic functions The Euler $\Gamma$-function The Riemann $\zeta$-function The theory of conformal mapping Index. /Rolf Nevanlinna & V Paatero Mathematics Functions of complex variables Linear Transformations Conformal Mapping 515.9 NEV 9780821891797 181113 20181113152445.0