See Taylor series in All languages combined, or Wiktionary
{ "etymology_text": "Named after English mathematician Brook Taylor, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician James Gregory.", "forms": [ { "form": "Taylor series", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "Taylor series" }, "expansion": "Taylor series (plural Taylor series)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Mandarin terms with redundant transliterations", "parents": [ "Terms with redundant transliterations", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Russian terms with non-redundant manual transliterations", "parents": [ "Terms with non-redundant manual transliterations", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Terms with Czech translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Danish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Hungarian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Mandarin translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Romanian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Russian translations", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Calculus", "orig": "en:Calculus", "parents": [ "Mathematical analysis", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "ref": "1978, [McGraw-Hill], Carl M. Bender, Steven A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Springer, published 1999, page 324:", "text": "A series solution about an ordinary point of a differential equation is always a Taylor series having a nonvanishing radius of convergence. A series solution about a singular point does not have this form (except in rare cases). Instead, it may be either a convergent series not in Taylor series form (such as a Frobenius series) or it may be a divergent series.", "type": "quote" }, { "ref": "1980, Suhas Patankar, Numerical Heat Transfer and Fluid Flow, Taylor & Francis (CRC Press), page 28:", "text": "The usual procedure for deriving finite-difference equations consists of approximating the derivatives in the differential equation via a truncated Taylor series.", "type": "quote" }, { "ref": "1998, Kenneth L. Judd, Numerical Methods in Economics, The MIT Press, page 197:", "text": "This function has its only singularity at x = 0, implying that the radius of convergence for the Taylor series around x = 1 is only unity.", "type": "quote" } ], "glosses": [ "A power series representation of given infinitely differentiable function f whose terms are calculated from the function's arbitrary order derivatives at given reference point a; the series f(a)+(f'(a))/(1!)(x-a)+(f(a))/(2!)(x-a)²+(f'(a))/(3!)(x-a)³+⋯=∑ₙ₌₀∞(f⁽ⁿ⁾(a))/(n!)(x-a)ⁿ." ], "hyponyms": [ { "sense": "power series of a function calculated from derivatives at a reference point", "word": "Maclaurin series" } ], "id": "en-Taylor_series-en-noun-kmWUJUxq", "links": [ [ "calculus", "calculus" ], [ "power series", "power series" ], [ "representation", "representation" ], [ "function", "function" ], [ "term", "term" ], [ "calculate", "calculate" ], [ "derivative", "derivative" ], [ "point", "point" ] ], "raw_glosses": [ "(calculus) A power series representation of given infinitely differentiable function f whose terms are calculated from the function's arbitrary order derivatives at given reference point a; the series f(a)+(f'(a))/(1!)(x-a)+(f(a))/(2!)(x-a)²+(f'(a))/(3!)(x-a)³+⋯=∑ₙ₌₀∞(f⁽ⁿ⁾(a))/(n!)(x-a)ⁿ." ], "synonyms": [ { "word": "Taylor's series" } ], "topics": [ "calculus", "mathematics", "sciences" ], "translations": [ { "code": "cmn", "lang": "Chinese Mandarin", "sense": "power series of a function calculated from derivatives at a reference point", "word": "泰勒展開式" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "Tàilè zhǎnkāishì", "sense": "power series of a function calculated from derivatives at a reference point", "word": "泰勒展开式" }, { "code": "cs", "lang": "Czech", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "feminine" ], "word": "Taylorova řada" }, { "code": "da", "lang": "Danish", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "common-gender" ], "word": "Taylorrække" }, { "code": "de", "lang": "German", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "feminine" ], "word": "Taylorreihe" }, { "code": "hu", "lang": "Hungarian", "sense": "power series of a function calculated from derivatives at a reference point", "word": "Taylor-sor" }, { "code": "it", "lang": "Italian", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "feminine" ], "word": "serie di Taylor" }, { "code": "ro", "lang": "Romanian", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "feminine" ], "word": "serie Taylor" }, { "code": "ru", "lang": "Russian", "roman": "rjad Tɛ́jlora", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "masculine" ], "word": "ряд Те́йлора" } ], "wikipedia": [ "Brook Taylor", "James Gregory (mathematician)", "Taylor series" ] } ], "word": "Taylor series" }
{ "etymology_text": "Named after English mathematician Brook Taylor, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician James Gregory.", "forms": [ { "form": "Taylor series", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "Taylor series" }, "expansion": "Taylor series (plural Taylor series)", "name": "en-noun" } ], "hyponyms": [ { "sense": "power series of a function calculated from derivatives at a reference point", "word": "Maclaurin series" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "English countable nouns", "English entries with incorrect language header", "English eponyms", "English lemmas", "English multiword terms", "English nouns", "English terms with quotations", "Entries with translation boxes", "Mandarin terms with redundant transliterations", "Pages with 1 entry", "Pages with entries", "Russian terms with non-redundant manual transliterations", "Terms with Czech translations", "Terms with Danish translations", "Terms with German translations", "Terms with Hungarian translations", "Terms with Italian translations", "Terms with Mandarin translations", "Terms with Romanian translations", "Terms with Russian translations", "en:Calculus" ], "examples": [ { "ref": "1978, [McGraw-Hill], Carl M. Bender, Steven A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Springer, published 1999, page 324:", "text": "A series solution about an ordinary point of a differential equation is always a Taylor series having a nonvanishing radius of convergence. A series solution about a singular point does not have this form (except in rare cases). Instead, it may be either a convergent series not in Taylor series form (such as a Frobenius series) or it may be a divergent series.", "type": "quote" }, { "ref": "1980, Suhas Patankar, Numerical Heat Transfer and Fluid Flow, Taylor & Francis (CRC Press), page 28:", "text": "The usual procedure for deriving finite-difference equations consists of approximating the derivatives in the differential equation via a truncated Taylor series.", "type": "quote" }, { "ref": "1998, Kenneth L. Judd, Numerical Methods in Economics, The MIT Press, page 197:", "text": "This function has its only singularity at x = 0, implying that the radius of convergence for the Taylor series around x = 1 is only unity.", "type": "quote" } ], "glosses": [ "A power series representation of given infinitely differentiable function f whose terms are calculated from the function's arbitrary order derivatives at given reference point a; the series f(a)+(f'(a))/(1!)(x-a)+(f(a))/(2!)(x-a)²+(f'(a))/(3!)(x-a)³+⋯=∑ₙ₌₀∞(f⁽ⁿ⁾(a))/(n!)(x-a)ⁿ." ], "links": [ [ "calculus", "calculus" ], [ "power series", "power series" ], [ "representation", "representation" ], [ "function", "function" ], [ "term", "term" ], [ "calculate", "calculate" ], [ "derivative", "derivative" ], [ "point", "point" ] ], "raw_glosses": [ "(calculus) A power series representation of given infinitely differentiable function f whose terms are calculated from the function's arbitrary order derivatives at given reference point a; the series f(a)+(f'(a))/(1!)(x-a)+(f(a))/(2!)(x-a)²+(f'(a))/(3!)(x-a)³+⋯=∑ₙ₌₀∞(f⁽ⁿ⁾(a))/(n!)(x-a)ⁿ." ], "topics": [ "calculus", "mathematics", "sciences" ], "wikipedia": [ "Brook Taylor", "James Gregory (mathematician)", "Taylor series" ] } ], "synonyms": [ { "word": "Taylor's series" } ], "translations": [ { "code": "cmn", "lang": "Chinese Mandarin", "sense": "power series of a function calculated from derivatives at a reference point", "word": "泰勒展開式" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "Tàilè zhǎnkāishì", "sense": "power series of a function calculated from derivatives at a reference point", "word": "泰勒展开式" }, { "code": "cs", "lang": "Czech", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "feminine" ], "word": "Taylorova řada" }, { "code": "da", "lang": "Danish", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "common-gender" ], "word": "Taylorrække" }, { "code": "de", "lang": "German", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "feminine" ], "word": "Taylorreihe" }, { "code": "hu", "lang": "Hungarian", "sense": "power series of a function calculated from derivatives at a reference point", "word": "Taylor-sor" }, { "code": "it", "lang": "Italian", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "feminine" ], "word": "serie di Taylor" }, { "code": "ro", "lang": "Romanian", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "feminine" ], "word": "serie Taylor" }, { "code": "ru", "lang": "Russian", "roman": "rjad Tɛ́jlora", "sense": "power series of a function calculated from derivatives at a reference point", "tags": [ "masculine" ], "word": "ряд Те́йлора" } ], "word": "Taylor series" }
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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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