See analytic function on Wiktionary
Download JSON data for analytic function meaning in All languages combined (6.4kB)
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"text": "There is a large and important literature concerned with the question of how to characterize precisely the boundary values of analytic functions. For example, when the analytic functions are of Hardy Class H#x2A; in a half plane, then their boundary values are attained in the L2 norm and, in fact, the analytic function can be reproduced by a Cauchy integral of the boundary value.",
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"text": "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,\nThus 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."
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"text": "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,\nWe review some results on regularity on the boundary in spaces of analytic functions on the unit disk connected with backward shift invariant subspaces in Hᵖ."
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"Any smooth (infinitely differentiable) function f, defined on an open set D⊆ℂ( textit or⊆ℝ), whose value in some neighbourhood of any given point x_0∈D is given by the Taylor series ∑ₙ₌₀ ᪲(f⁽ⁿ⁾(x_0))/(n!)(x-x_0)ⁿ."
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"(mathematical analysis) Any smooth (infinitely differentiable) function f, defined on an open set D⊆ℂ( textit or⊆ℝ), whose value in some neighbourhood of any given point x_0∈D is given by the Taylor series ∑ₙ₌₀ ᪲(f⁽ⁿ⁾(x_0))/(n!)(x-x_0)ⁿ."
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"translations": [
{
"_dis1": "43 57",
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "mathematical function",
"word": "解析函數"
},
{
"_dis1": "43 57",
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"roman": "jiěxī hánshù",
"sense": "mathematical function",
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"sense": "mathematical function",
"word": "analyyttinen funktio"
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"sense": "mathematical function",
"word": "analitikus függvény"
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"word": "suriing kabisa"
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"text": "There is a large and important literature concerned with the question of how to characterize precisely the boundary values of analytic functions. For example, when the analytic functions are of Hardy Class H#x2A; in a half plane, then their boundary values are attained in the L2 norm and, in fact, the analytic function can be reproduced by a Cauchy integral of the boundary value.",
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},
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"text": "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,\nWe review some results on regularity on the boundary in spaces of analytic functions on the unit disk connected with backward shift invariant subspaces in Hᵖ."
}
],
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"Any smooth (infinitely differentiable) function f, defined on an open set D⊆ℂ( textit or⊆ℝ), whose value in some neighbourhood of any given point x_0∈D is given by the Taylor series ∑ₙ₌₀ ᪲(f⁽ⁿ⁾(x_0))/(n!)(x-x_0)ⁿ."
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"code": "cmn",
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"sense": "mathematical function",
"word": "解析函數"
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{
"code": "cmn",
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"roman": "jiěxī hánshù",
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{
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"word": "analytická funkce"
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{
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"lang": "Finnish",
"sense": "mathematical function",
"word": "analyyttinen funktio"
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{
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"sense": "mathematical function",
"word": "analitikus függvény"
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"word": "raunfágað fall"
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{
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"sense": "mathematical function",
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"word": "função analítica"
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"sense": "mathematical function",
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"word": "analytisk funktion"
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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