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Lecture# Holomorphic Functions: Taylor Series Expansion

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This lecture covers the basic properties of holomorphic maps, focusing on Taylor series expansions. It explains the concept of Taylor series expansion for holomorphic functions and its applications, such as convergence radius and uniqueness. The lecture also introduces the lemma related to holomorphic functions and their convergence. The proof of the properties of holomorphic maps is discussed, emphasizing the importance of Taylor series expansions in complex analysis.

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Related concepts (263)

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In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in , such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex manifold), and an almost complex manifold. Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds.

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