See Maclaurin series in All languages combined, or Wiktionary
{
"etymology_text": "Named after Scottish mathematician Colin Maclaurin (1698-1746), who made extensive use of the series.",
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"tags": [
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"lang_code": "en",
"pos": "noun",
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"examples": [
{
"ref": "1953, Raymond Lyttleton, The Stability of Rotating Liquid Masses, Paperback edition, Cambridge University Press, published 2013, page 42:",
"text": "Analytically there are, of course, two Jacobi series branching off the Maclaurin series, but they are geometrically and physically identical, and involve only an interchange of a and b.",
"type": "quote"
},
{
"text": "1995, Ralph P. Boas, Gerald L. Alexanderson (editor), Dale H. Mugler (editor), Lion Hunting and Other Mathematical Pursuits, Mathematical Association of America, page 88,\nIf the Maclaurin series of f and g converge for |z| < r and g(z) ≠ 0 for 0 ≤ |z| < r, then if the Maclaurin series for f is divided by the Maclaurin series for g by long division (as if the series were polynomials), the resulting series represents f / g for |z| < r."
},
{
"ref": "1997, Frank Smithies, Cauchy and the Creation of Complex Function Theory, Cambridge University Press, page 203:",
"text": "It was almost as a by-product of this work that, in the first Turin memoir, he proved the convergence of the Maclaurin series of a function up to the singularity nearest to the origin (Section 7.5); it was in this context that he created what he called 'calculus of limits', later known as the method of majorants.",
"type": "quote"
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],
"glosses": [
"Any Taylor series that is centred at 0 (i.e., for which the origin is the reference point used to derive the series from its associated function); for a given infinitely differentiable complex function f, the power series f(0)+(f'(0))/(1!)x+(f(0))/(2!)x²+(f'(0))/(3!)x³+⋯=∑ₙ₌₀ ᪲(f⁽ⁿ⁾(0))/(n!),xⁿ."
],
"hypernyms": [
{
"sense": "Taylor series centred at 0",
"word": "power series"
},
{
"sense": "Taylor series centred at 0",
"word": "Taylor series"
}
],
"id": "en-Maclaurin_series-en-noun-6emRcdRC",
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"raw_glosses": [
"(calculus) Any Taylor series that is centred at 0 (i.e., for which the origin is the reference point used to derive the series from its associated function); for a given infinitely differentiable complex function f, the power series f(0)+(f'(0))/(1!)x+(f(0))/(2!)x²+(f'(0))/(3!)x³+⋯=∑ₙ₌₀ ᪲(f⁽ⁿ⁾(0))/(n!),xⁿ."
],
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"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "Taylor series centred at 0",
"word": "馬克勞林級數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "Taylor series centred at 0",
"word": "马克劳林级数"
},
{
"code": "da",
"lang": "Danish",
"sense": "Taylor series centred at 0",
"word": "Maclaurinrække"
},
{
"code": "de",
"lang": "German",
"sense": "Taylor series centred at 0",
"tags": [
"feminine"
],
"word": "Maclaurin-Reihe"
},
{
"code": "de",
"lang": "German",
"sense": "Taylor series centred at 0",
"tags": [
"feminine"
],
"word": "maclaurinsche Reihe"
},
{
"code": "it",
"lang": "Italian",
"sense": "Taylor series centred at 0",
"tags": [
"feminine"
],
"word": "serie di Maclaurin"
},
{
"code": "ja",
"lang": "Japanese",
"sense": "Taylor series centred at 0",
"word": "マクローリン級数"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "Taylor series centred at 0",
"tags": [
"feminine"
],
"word": "serie Maclaurin"
}
],
"wikipedia": [
"Colin Maclaurin",
"Maclaurin series"
]
}
],
"word": "Maclaurin series"
}
{
"etymology_text": "Named after Scottish mathematician Colin Maclaurin (1698-1746), who made extensive use of the series.",
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{
"sense": "Taylor series centred at 0",
"word": "power series"
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"lang_code": "en",
"pos": "noun",
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"examples": [
{
"ref": "1953, Raymond Lyttleton, The Stability of Rotating Liquid Masses, Paperback edition, Cambridge University Press, published 2013, page 42:",
"text": "Analytically there are, of course, two Jacobi series branching off the Maclaurin series, but they are geometrically and physically identical, and involve only an interchange of a and b.",
"type": "quote"
},
{
"text": "1995, Ralph P. Boas, Gerald L. Alexanderson (editor), Dale H. Mugler (editor), Lion Hunting and Other Mathematical Pursuits, Mathematical Association of America, page 88,\nIf the Maclaurin series of f and g converge for |z| < r and g(z) ≠ 0 for 0 ≤ |z| < r, then if the Maclaurin series for f is divided by the Maclaurin series for g by long division (as if the series were polynomials), the resulting series represents f / g for |z| < r."
},
{
"ref": "1997, Frank Smithies, Cauchy and the Creation of Complex Function Theory, Cambridge University Press, page 203:",
"text": "It was almost as a by-product of this work that, in the first Turin memoir, he proved the convergence of the Maclaurin series of a function up to the singularity nearest to the origin (Section 7.5); it was in this context that he created what he called 'calculus of limits', later known as the method of majorants.",
"type": "quote"
}
],
"glosses": [
"Any Taylor series that is centred at 0 (i.e., for which the origin is the reference point used to derive the series from its associated function); for a given infinitely differentiable complex function f, the power series f(0)+(f'(0))/(1!)x+(f(0))/(2!)x²+(f'(0))/(3!)x³+⋯=∑ₙ₌₀ ᪲(f⁽ⁿ⁾(0))/(n!),xⁿ."
],
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"(calculus) Any Taylor series that is centred at 0 (i.e., for which the origin is the reference point used to derive the series from its associated function); for a given infinitely differentiable complex function f, the power series f(0)+(f'(0))/(1!)x+(f(0))/(2!)x²+(f'(0))/(3!)x³+⋯=∑ₙ₌₀ ᪲(f⁽ⁿ⁾(0))/(n!),xⁿ."
],
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"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "Taylor series centred at 0",
"word": "馬克勞林級數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "Taylor series centred at 0",
"word": "马克劳林级数"
},
{
"code": "da",
"lang": "Danish",
"sense": "Taylor series centred at 0",
"word": "Maclaurinrække"
},
{
"code": "de",
"lang": "German",
"sense": "Taylor series centred at 0",
"tags": [
"feminine"
],
"word": "Maclaurin-Reihe"
},
{
"code": "de",
"lang": "German",
"sense": "Taylor series centred at 0",
"tags": [
"feminine"
],
"word": "maclaurinsche Reihe"
},
{
"code": "it",
"lang": "Italian",
"sense": "Taylor series centred at 0",
"tags": [
"feminine"
],
"word": "serie di Maclaurin"
},
{
"code": "ja",
"lang": "Japanese",
"sense": "Taylor series centred at 0",
"word": "マクローリン級数"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "Taylor series centred at 0",
"tags": [
"feminine"
],
"word": "serie Maclaurin"
}
],
"word": "Maclaurin 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 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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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