See analytic function on Wiktionary
{
"derived": [
{
"_dis1": "46 54",
"word": "complex analytic function"
},
{
"_dis1": "46 54",
"word": "real analytic function"
}
],
"forms": [
{
"form": "analytic functions",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "analytic function (plural analytic functions)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Functions",
"orig": "en:Functions",
"parents": [
"Algebra",
"Calculus",
"Geometry",
"Mathematical analysis",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematical analysis",
"orig": "en:Mathematical analysis",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "52 48",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "67 33",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "58 42",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "64 36",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "63 37",
"kind": "other",
"name": "Terms with Czech translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "66 34",
"kind": "other",
"name": "Terms with Finnish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "65 35",
"kind": "other",
"name": "Terms with Icelandic translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "53 47",
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "64 36",
"kind": "other",
"name": "Terms with Portuguese translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "65 35",
"kind": "other",
"name": "Terms with Serbo-Croatian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "66 34",
"kind": "other",
"name": "Terms with Swedish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "64 36",
"kind": "other",
"name": "Terms with Tagalog translations",
"parents": [],
"source": "w+disamb"
}
],
"examples": [
{
"ref": "1966, E. J. Beltrami, M. R. Wohlers, Distributions and the Boundary Values of Analytic Functions, Academic Press, page vii:",
"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#42; 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.",
"type": "quote"
},
{
"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."
},
{
"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."
}
],
"glosses": [
"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."
],
"hypernyms": [
{
"_dis1": "63 37",
"sense": "analysis",
"word": "function"
}
],
"hyponyms": [
{
"_dis1": "63 37",
"sense": "analysis",
"word": "complex analytic function"
},
{
"_dis1": "63 37",
"sense": "analysis",
"word": "monogenic analytic function"
},
{
"_dis1": "63 37",
"sense": "analysis",
"word": "real analytic function"
}
],
"id": "en-analytic_function-en-noun-h9p1SwMY",
"links": [
[
"mathematical analysis",
"mathematical analysis"
],
[
"smooth",
"smooth"
],
[
"function",
"function"
],
[
"open set",
"open set"
],
[
"neighbourhood",
"neighbourhood"
],
[
"Taylor series",
"Taylor series"
]
],
"raw_glosses": [
"(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."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Databases",
"orig": "en:Databases",
"parents": [
"Computing",
"Technology",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "52 48",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "41 59",
"kind": "other",
"name": "Terms with Hungarian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "53 47",
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"window function"
],
"id": "en-analytic_function-en-noun--FlZm7bt",
"links": [
[
"database",
"database"
],
[
"window function",
"window function"
]
],
"raw_glosses": [
"(databases) window function"
],
"topics": [
"computing",
"databases",
"engineering",
"mathematics",
"natural-sciences",
"physical-sciences",
"sciences"
]
}
],
"translations": [
{
"_dis1": "50 50",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "jiěxī hánshù",
"sense": "mathematical function",
"word": "解析函數 /解析函数"
},
{
"_dis1": "50 50",
"code": "cs",
"lang": "Czech",
"sense": "mathematical function",
"tags": [
"feminine"
],
"word": "analytická funkce"
},
{
"_dis1": "50 50",
"code": "fi",
"lang": "Finnish",
"sense": "mathematical function",
"word": "analyyttinen funktio"
},
{
"_dis1": "50 50",
"code": "hu",
"lang": "Hungarian",
"sense": "mathematical function",
"word": "analitikus függvény"
},
{
"_dis1": "50 50",
"code": "is",
"lang": "Icelandic",
"sense": "mathematical function",
"tags": [
"neuter"
],
"word": "raunfágað fall"
},
{
"_dis1": "50 50",
"code": "pt",
"lang": "Portuguese",
"sense": "mathematical function",
"tags": [
"feminine"
],
"word": "função analítica"
},
{
"_dis1": "50 50",
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "mathematical function",
"tags": [
"feminine"
],
"word": "analitička funkcija"
},
{
"_dis1": "50 50",
"code": "sv",
"lang": "Swedish",
"sense": "mathematical function",
"tags": [
"common-gender"
],
"word": "analytisk funktion"
},
{
"_dis1": "50 50",
"code": "tl",
"lang": "Tagalog",
"sense": "mathematical function",
"word": "suriing kabisa"
}
],
"wikipedia": [
"analytic function"
],
"word": "analytic function"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with Czech translations",
"Terms with Finnish translations",
"Terms with Hungarian translations",
"Terms with Icelandic translations",
"Terms with Mandarin translations",
"Terms with Portuguese translations",
"Terms with Serbo-Croatian translations",
"Terms with Swedish translations",
"Terms with Tagalog translations"
],
"derived": [
{
"word": "complex analytic function"
},
{
"word": "real analytic function"
}
],
"forms": [
{
"form": "analytic functions",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "analytic function (plural analytic functions)",
"name": "en-noun"
}
],
"hypernyms": [
{
"sense": "analysis",
"word": "function"
}
],
"hyponyms": [
{
"sense": "analysis",
"word": "complex analytic function"
},
{
"sense": "analysis",
"word": "monogenic analytic function"
},
{
"sense": "analysis",
"word": "real analytic function"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English terms with quotations",
"en:Functions",
"en:Mathematical analysis"
],
"examples": [
{
"ref": "1966, E. J. Beltrami, M. R. Wohlers, Distributions and the Boundary Values of Analytic Functions, Academic Press, page vii:",
"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#42; 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.",
"type": "quote"
},
{
"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."
},
{
"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."
}
],
"glosses": [
"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."
],
"links": [
[
"mathematical analysis",
"mathematical analysis"
],
[
"smooth",
"smooth"
],
[
"function",
"function"
],
[
"open set",
"open set"
],
[
"neighbourhood",
"neighbourhood"
],
[
"Taylor series",
"Taylor series"
]
],
"raw_glosses": [
"(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."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Databases"
],
"glosses": [
"window function"
],
"links": [
[
"database",
"database"
],
[
"window function",
"window function"
]
],
"raw_glosses": [
"(databases) window function"
],
"topics": [
"computing",
"databases",
"engineering",
"mathematics",
"natural-sciences",
"physical-sciences",
"sciences"
]
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "jiěxī hánshù",
"sense": "mathematical function",
"word": "解析函數 /解析函数"
},
{
"code": "cs",
"lang": "Czech",
"sense": "mathematical function",
"tags": [
"feminine"
],
"word": "analytická funkce"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "mathematical function",
"word": "analyyttinen funktio"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "mathematical function",
"word": "analitikus függvény"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "mathematical function",
"tags": [
"neuter"
],
"word": "raunfágað fall"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "mathematical function",
"tags": [
"feminine"
],
"word": "função analítica"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "mathematical function",
"tags": [
"feminine"
],
"word": "analitička funkcija"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "mathematical function",
"tags": [
"common-gender"
],
"word": "analytisk funktion"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "mathematical function",
"word": "suriing kabisa"
}
],
"wikipedia": [
"analytic function"
],
"word": "analytic function"
}
Download raw JSONL data for analytic function meaning in All languages combined (5.0kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-02-17 from the enwiktionary dump dated 2025-02-02 using wiktextract (ca09fec and c40eb85). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.