Category:Complex analysis

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Complex analysis is the branch of mathematics investigating holomorphic functions, i.e. functions which are defined in some region of the complex plane, take complex values, and are differentiable as complex functions. Complex differentiability has much stronger consequences than usual (real) differentiability. For instance, every holomorphic function is representable as power series in every open disc in its domain of definition, and is therefore analytic. In particular, holomorphic functions are infinitely differentiable, a fact that is far from true for real differentiable functions. Most elementary functions, such as all polynomials, the exponential function, and the trigonometric functions, are holomorphic. See also : holomorphic sheaves and vector bundles.

Subcategories

There are 8 subcategories to this category shown below (more may be shown on subsequent pages).

A Analytic number theory C Conformal mapping

H Hardy spaces Harmonic functions M Modular forms

R Riemann surfaces S Several complex variables Special functions

Pages in category "Complex analysis"

There are 126 pages in this section of this category.

List of complex analysis topics * Complex analysis A Algebraic geometry and analytic geometry Almost periodic function Analytic capacity Analytic continuation Analytic function Analytic variety Antiderivative (complex analysis) Antiholomorphic function Argument principle B Bicoherence Bifurcation locus Bispectrum Blaschke product Borel–Carathéodory theorem Branch point Bromwich integral C Carlson's theorem Cartan's theorems A and B Cauchy's integral formula Cauchy's integral theorem Cauchy-Riemann equations Cayley transform Complex logarithm Cousin problems Critical line theorem D De Branges function De Branges' theorem De Moivre's formula Dessin d'enfant Disk algebra Domain coloring Doubly-periodic function E Edge-of-the-wedge theorem Entire function Essential singularity Estimation lemma Euler's formula Euler's identity Exponential function Exponential sheaf sequence

F Fundamental recurrence formulas Fundamental theorem of algebra G Generalized continued fraction Geometric function theory H Hadamard three-circle theorem Hankel contour Hardy's theorem Holomorphic function Holomorphic functional calculus Holomorphic sheaf Holomorphically separable Hurwitz's theorem Hyperfunction I Identity theorem Imaginary number Isolated singularity Iterated monodromy group J Jensen's formula Jordan's lemma K Kramers-Kronig relation L Lacunary value Landau's constants Laurent series Lindelöf's theorem Line integral Liouville's theorem (complex analysis) List of Fourier-related transforms Logarithmic derivative Logarithmic form M Maximum modulus principle Mellin inversion theorem Mellin transform Mergelyan's theorem Meromorphic function Methods of contour integration Mittag-Leffler's theorem Monodromy Montel's theorem Morera's theorem Motor variable N Nachbin's theorem Normal family Nörlund-Rice integral

O Open mapping theorem P Paley–Wiener theorem Partial fractions in complex analysis Periodic points of complex quadratic mappings Perron's formula Phragmén-Lindelöf principle Picard theorem Pole (complex analysis) Polynomial Polynomial function theorems for zeros Positive-definite function Principal branch Principal part Principal value Proof that holomorphic functions are analytic Q Quasiperiodic function R Radius of convergence Ramification Regular part Regular singular point Removable singularity Residue (complex analysis) Residue theorem Rothe-Hagen identity Rouché's theorem Runge's theorem S Schwarz lemma Schwarz reflection principle Several complex variables Siegel upper half-plane Subharmonic function T Titchmarsh convolution theorem U Univalent function Upper half-plane V Value distribution theory of holomorphic functions Vector bundle W Weierstrass factorization theorem Weierstrass–Casorati theorem Winding number Z Zero (complex analysis) Zero-product property

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Categories: Mathematical analysis | Multivariate calculus

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