Category:Complex analysis

From Wikipedia, the free encyclopedia

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.ca:Categoria:Anàlisi complexa cs:Kategorie:Komplexní analýza de:Kategorie:Funktionentheorie es:Categoría:Análisis complejo eo:Kategorio:Kompleksa analitiko fa:رده:آنالیز مختلط fr:Catégorie:Analyse complexe it:Categoria:Analisi complessa he:קטגוריה:אנליזה מרוכבת pt:Categoria:Análise complexa ru:Категория:Комплексный анализ sl:Kategorija:Kompleksna analiza sv:Kategori:Komplex analys th:หมวดหมู่:การวิเคราะห์เชิงซ้อน