analytic function

== English == === Noun === analytic function (plural analytic functions) (mathematical analysis) Any smooth (infinitely differentiable) function f {\displaystyle f} , defined on an open set D ⊆ C ( or ⊆ R ) {\displaystyle D\subseteq \mathbb {C} \ ({\textit {or}}\subseteq \mathbb {R} )} , whose value in some neighbourhood of any given point x 0 ∈ D {\displaystyle x_{0}\in D} is given by the Taylor series ∑ n = 0 ∞ f ( n ) ( x 0 ) n ! ( x − x 0 ) n {\displaystyle \textstyle \sum _{n=0}^{\infty }{\frac {f^{(n)}(x_{0})}{n!}}(x-x_{0})^{n}} . 2000, Vladimir V. Mityushev, Sergei V. Rogosin, Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions: Theory and Applications, Chapman & Hall / CRC, page v, Thus we have limited ourselves by boundary value problems for analytic functions, and some related problems. The constructive ideas are always in our mind, so, the basic goal of this book is to be useful for experts in analytic function theory and for nonspecialists in it, and even for non-mathematicians who apply these methods in their research. 2010, Emmanuel Fricain, Andreas Hartmann, Regularity on the Boundary in Spaces of Holomorphic Functions on the Unit Disk, Javad Mashreghi, Thomas Ransford, Kristian Seip (editors, Hilbert Spaces of Analytic Functions, American Mathematical Society, page 91, We review some results on regularity on the boundary in spaces of analytic functions on the unit disk connected with backward shift invariant subspaces in H p {\displaystyle H^{p}} . (databases) window function ==== Usage notes ==== In complex analysis, often used interchangeably with holomorphic function, although analytic function has broader context. ==== Hypernyms ==== (analysis): function ==== Hyponyms ==== (analysis): complex analytic function, monogenic analytic function, real analytic function ==== Derived terms ==== complex analytic function real analytic function ==== Translations ==== === Further reading === Holomorphic function on Wikipedia.Wikipedia