"power series" meaning in English

{
  "forms": [
    {
      "form": "power series",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "power series"
      },
      "expansion": "power series (plural power 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": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "formal power series"
        }
      ],
      "examples": [
        {
          "ref": "1983, Ian Stewart, David Tall, Complex Analysis, Cambridge University Press, page 259",
          "text": "Thus no single choice of z₀ will give a power series expansion of f(z) valid for all #x5C;textstylez#x5C;in#x5C;mathbb#x7B;C#x7D;#x5C;setminus#x5C;left#x5C;#x7B;-1,1#x5C;right#x5C;#x7D; even though f is analytic on this set.",
          "type": "quotation"
        },
        {
          "ref": "1988, Richard Courant, translated by E. J. McShane, Differential and Integral Calculus, 2nd edition, volume 1, Wiley, page 413",
          "text": "In this we may use as our starting-point a general discussion of the theory of power series with complex variables and complex coefficients. The construction of such a theory of power series offers no difficulty once we define the concept of limit in the domain of complex numbers; in fact, it follows the theory of real power series almost exactly.",
          "type": "quotation"
        },
        {
          "text": "1899, Oskar Bolza, The Theory of Functions, 2013, Reprint, Books on Demand, page 69,\nFrom this theorem (for which in many cases Cauchy's theorem on double sums may be substituted) follow easily the rules for the multiplication and division of power series, Taylor's theorem for power series along with the rules for differentiation of power series and series of power series."
        }
      ],
      "glosses": [
        "Any infinite series of the general form ∑ᵢ₌₀ ᪲a_i(x-c)ⁱ."
      ],
      "hyponyms": [
        {
          "word": "Maclaurin series"
        },
        {
          "word": "Taylor series"
        },
        {
          "word": "Laurent series"
        }
      ],
      "id": "en-power_series-en-noun-d~L7uZ8v",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "infinite",
          "infinite"
        ],
        [
          "series",
          "series"
        ]
      ],
      "raw_glosses": [
        "(mathematics, mathematical analysis) Any infinite series of the general form ∑ᵢ₌₀ ᪲a_i(x-c)ⁱ."
      ],
      "synonyms": [
        {
          "tags": [
            "attributive"
          ],
          "word": "power-series"
        }
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "cs",
          "lang": "Czech",
          "sense": "Translations",
          "word": "mocninná řada"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "Potenzreihe"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "Translations",
          "tags": [
            "masculine"
          ],
          "word": "szereg potęgowy"
        },
        {
          "code": "ro",
          "lang": "Romanian",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "serie de puteri"
        }
      ],
      "wikipedia": [
        "power series"
      ]
    }
  ],
  "word": "power series"
}

{
  "derived": [
    {
      "word": "formal power series"
    }
  ],
  "forms": [
    {
      "form": "power series",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "power series"
      },
      "expansion": "power series (plural power series)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "word": "Maclaurin series"
    },
    {
      "word": "Taylor series"
    },
    {
      "word": "Laurent series"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "Translation table header lacks gloss",
        "en:Mathematical analysis",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "1983, Ian Stewart, David Tall, Complex Analysis, Cambridge University Press, page 259",
          "text": "Thus no single choice of z₀ will give a power series expansion of f(z) valid for all #x5C;textstylez#x5C;in#x5C;mathbb#x7B;C#x7D;#x5C;setminus#x5C;left#x5C;#x7B;-1,1#x5C;right#x5C;#x7D; even though f is analytic on this set.",
          "type": "quotation"
        },
        {
          "ref": "1988, Richard Courant, translated by E. J. McShane, Differential and Integral Calculus, 2nd edition, volume 1, Wiley, page 413",
          "text": "In this we may use as our starting-point a general discussion of the theory of power series with complex variables and complex coefficients. The construction of such a theory of power series offers no difficulty once we define the concept of limit in the domain of complex numbers; in fact, it follows the theory of real power series almost exactly.",
          "type": "quotation"
        },
        {
          "text": "1899, Oskar Bolza, The Theory of Functions, 2013, Reprint, Books on Demand, page 69,\nFrom this theorem (for which in many cases Cauchy's theorem on double sums may be substituted) follow easily the rules for the multiplication and division of power series, Taylor's theorem for power series along with the rules for differentiation of power series and series of power series."
        }
      ],
      "glosses": [
        "Any infinite series of the general form ∑ᵢ₌₀ ᪲a_i(x-c)ⁱ."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "infinite",
          "infinite"
        ],
        [
          "series",
          "series"
        ]
      ],
      "raw_glosses": [
        "(mathematics, mathematical analysis) Any infinite series of the general form ∑ᵢ₌₀ ᪲a_i(x-c)ⁱ."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "power series"
      ]
    }
  ],
  "synonyms": [
    {
      "tags": [
        "attributive"
      ],
      "word": "power-series"
    }
  ],
  "translations": [
    {
      "code": "cs",
      "lang": "Czech",
      "sense": "Translations",
      "word": "mocninná řada"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "Potenzreihe"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "Translations",
      "tags": [
        "masculine"
      ],
      "word": "szereg potęgowy"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "serie de puteri"
    }
  ],
  "word": "power series"
}