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  2. Category:Theorems in complex analysis - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_in...

    Pages in category "Theorems in complex analysis" The following 110 pages are in this category, out of 110 total. This list may not reflect recent changes. A.

  3. Complex analysis - Wikipedia

    en.wikipedia.org/wiki/Complex_analysis

    Augustin-Louis Cauchy, one of the founders of complex analysis. Complex analysis is one of the classical branches in mathematics, with roots in the 18th century and just prior. Important mathematicians associated with complex numbers include Euler, Gauss, Riemann, Cauchy, Gösta Mittag-Leffler, Weierstrass, and many more in the 20th century.

  4. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Bloch's theorem (complex analysis) Blondel's theorem (electric power) Blum's speedup theorem (computational complexity theory) Bôcher's theorem (complex analysis) Bochner's tube theorem (complex analysis) Bogoliubov–Parasyuk theorem (quantum field theory) Bohr–Mollerup theorem (gamma function) Bohr–van Leeuwen theorem

  5. Liouville's theorem (complex analysis) - Wikipedia

    en.wikipedia.org/wiki/Liouville's_theorem...

    In complex analysis, Liouville's theorem, named after Joseph Liouville (although the theorem was first proven by Cauchy in 1844 [1]), states that every bounded entire function must be constant. That is, every holomorphic function f {\displaystyle f} for which there exists a positive number M {\displaystyle M} such that | f ( z ) | ≤ M ...

  6. Cauchy's integral theorem - Wikipedia

    en.wikipedia.org/wiki/Cauchy's_integral_theorem

    In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane.

  7. Open mapping theorem (complex analysis) - Wikipedia

    en.wikipedia.org/wiki/Open_mapping_theorem...

    In complex analysis, the open mapping theorem states that if is a domain of the complex plane and : is a non-constant holomorphic function, then is an open map (i.e. it sends open subsets of to open subsets of , and we have invariance of domain.).

  8. Hurwitz's theorem (complex analysis) - Wikipedia

    en.wikipedia.org/wiki/Hurwitz's_theorem_(complex...

    Hurwitz's theorem is used in the proof of the Riemann mapping theorem, [2] and also has the following two corollaries as an immediate consequence: . Let G be a connected, open set and {f n} a sequence of holomorphic functions which converge uniformly on compact subsets of G to a holomorphic function f.

  9. Function of several complex variables - Wikipedia

    en.wikipedia.org/wiki/Function_of_several...

    As in complex analysis of functions of one variable, which is the case n = 1, the functions studied are holomorphic or complex analytic so that, locally, they are power series in the variables z i. Equivalently, they are locally uniform limits of polynomials; or locally square-integrable solutions to the n-dimensional Cauchy–Riemann equations.