Analytic function

English

Noun

1. Template:Lb Any smooth (infinitely differentiable) function $f$, defined on an open set Template:C $D\subseteq ℂ(\mathit{\text{or}}\subseteq ℝ)$, whose value in some neighbourhood of any given point $x_0\in D$ is given by the Taylor series ${\sum }_{n=0}^{\mathrm{\infty }}\frac{f^{(n)}(x_0)}{n!}(x-x_0{)}^n$.
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   • 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, Template:W, 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 $H^p$.

2. Template:Lb window function

Usage notes

In complex analysis, often used interchangeably with Template:M function, although analytic function has broader context.

Hypernyms

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Hyponyms

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Derived terms

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Translations

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