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45 Meromorphic Functions Lecture 4 Complex Analysis Rataional and Meromorphic Asymptotics
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Lecture slides: • http://ac.cs.princeton.edu/lectures/l... • Full course playlist • • Playlist • Lecture 4: Complex Analysis, Rational and Meromorphic Asymptotics. • We consider basic principles of complex analysis, including analytic functions (which can be expanded as power series in a region); singularities (points where functions cease to be analytic); rational functions (the ratio of two polynomials) and meromorphic functions (the ratio of two analytic functions). The heart of the matter is complex integration and Cauchy's theorem, which relates coefficients in a function's expansion to its behavior near singularities. The discussion culminates in a general transfer theorem that gives asymptotic values of coefficients for meromorphic (and rational) functions.
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