"Maclaurin series" meaning in All languages combined

{
  "etymology_text": "Named after Scottish mathematician Colin Maclaurin (1698-1746), who made extensive use of the series.",
  "forms": [
    {
      "form": "Maclaurin series",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "Maclaurin series"
      },
      "expansion": "Maclaurin series (plural Maclaurin 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": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "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": "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": "quotation"
        },
        {
          "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": "quotation"
        }
      ],
      "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",
      "links": [
        [
          "calculus",
          "calculus"
        ],
        [
          "Taylor series",
          "Taylor series"
        ],
        [
          "origin",
          "origin"
        ],
        [
          "complex function",
          "complex function"
        ],
        [
          "power series",
          "power series"
        ]
      ],
      "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."
      ],
      "topics": [
        "calculus",
        "mathematics",
        "sciences"
      ],
      "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.",
  "forms": [
    {
      "form": "Maclaurin series",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "Maclaurin series"
      },
      "expansion": "Maclaurin series (plural Maclaurin series)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "sense": "Taylor series centred at 0",
      "word": "power series"
    },
    {
      "sense": "Taylor series centred at 0",
      "word": "Taylor series"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "English terms with quotations",
        "en:Calculus"
      ],
      "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": "quotation"
        },
        {
          "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": "quotation"
        }
      ],
      "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."
      ],
      "links": [
        [
          "calculus",
          "calculus"
        ],
        [
          "Taylor series",
          "Taylor series"
        ],
        [
          "origin",
          "origin"
        ],
        [
          "complex function",
          "complex function"
        ],
        [
          "power series",
          "power series"
        ]
      ],
      "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."
      ],
      "topics": [
        "calculus",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Colin Maclaurin",
        "Maclaurin series"
      ]
    }
  ],
  "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"
}