"gamma function" meaning in English

See gamma function in All languages combined, or Wiktionary

Noun

Forms: gamma functions [plural]
Etymology: The function itself was initially defined as an integral (in modern representation, Γ(x)=∫₀ ᪲e⁻ᵗtˣ⁻¹dt) for positive real x by Swiss mathematician Leonhard Euler in 1730. The name derives from the notation, Γ(x), which was introduced by Adrien-Marie Legendre (1752—1833) (he referred to it, however, as the Eulerian integral of the second kind). Both Euler's integral and Legendre's notation shift the argument with respect to the factorial, so that for integer n>0, Γ(n) = (n−1)!. Carl Friedrich Gauss preferred π(x), with no shift, but Legendre's notation prevailed. Generalisation to non-integer negative and to complex numbers was achieved by analytic continuation. Head templates: {{en-noun}} gamma function (plural gamma functions)
  1. (mathematical analysis) A meromorphic function which generalizes the notion of factorial to complex numbers and has singularities at the nonpositive integers; any of certain generalizations or analogues of said function, such as extend the factorial to domains other than the complex numbers. Wikipedia link: Adrien-Marie Legendre, American Mathematical Monthly, Carl Friedrich Gauss, Leonhard Euler Categories (topical): Functions, Mathematical analysis Synonyms (function that extends the domain of the factorial): Euler integral of the second kind (english: regarded as an integral) Hypernyms: function Hyponyms: digamma function, incomplete gamma function, polygamma function, trigamma function Translations (function which generalizes the notion of a factorial): fonction gamma [feminine] (French), Gammafunktion [feminine] (German), gamma-függvény (Hungarian), funzione Gamma [feminine] (Italian), funzione Gamma di Eulero [feminine] (Italian), ガンマ関数 (ganma kansū) (Japanese), تابع گاما (tâbe'-e gâmâ) (Persian), funkcja gamma [feminine] (Polish), га́мма-фу́нкция (gámma-fúnkcija) [feminine] (Russian), gammafunktionen [common-gender] (Swedish), Eulers gammafunktion [common-gender] (Swedish), gama fonksiyonu (Turkish)
    Sense id: en-gamma_function-en-noun-CXnk7wy2 Categories (other): English entries with incorrect language header, English entries with topic categories using raw markup, English terms with non-redundant non-automated sortkeys Topics: mathematical-analysis, mathematics, sciences

Inflected forms

Download JSON data for gamma function meaning in English (6.2kB)

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  "etymology_text": "The function itself was initially defined as an integral (in modern representation, Γ(x)=∫₀ ᪲e⁻ᵗtˣ⁻¹dt) for positive real x by Swiss mathematician Leonhard Euler in 1730. The name derives from the notation, Γ(x), which was introduced by Adrien-Marie Legendre (1752—1833) (he referred to it, however, as the Eulerian integral of the second kind). Both Euler's integral and Legendre's notation shift the argument with respect to the factorial, so that for integer n>0, Γ(n) = (n−1)!. Carl Friedrich Gauss preferred π(x), with no shift, but Legendre's notation prevailed. Generalisation to non-integer negative and to complex numbers was achieved by analytic continuation.",
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          "text": "Chapter 3 deals with the p-adic gamma function.",
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          "text": "2002, M. Aslam Chaudhry, Syed M. Zubair, On a Class of Incomplete Gamma Functions with Applications, Chapman & Hall / CRC Press, page 2,\nIn particular, the exponential, circular, and hyperbolic functions are rational combinations of gamma functions."
        },
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          "ref": "2007, Philip J. Davis, “Leonhard Euler's Integral: A Historical Profile of the Gamma Function”, in William Dunham, editor, The Genius of Euler: Reflections on His Life and Work, American Mathematical Society, page 167",
          "text": "We select one mathematical object, the gamma function, and show how it grew in concept and in content from the time of Euler to the recent mathematical treatise of Bourbaki, and how, in this growth, it partook of the general development of mathematics over the past two and a quarter centuries.",
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        "A meromorphic function which generalizes the notion of factorial to complex numbers and has singularities at the nonpositive integers; any of certain generalizations or analogues of said function, such as extend the factorial to domains other than the complex numbers."
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        {
          "word": "incomplete gamma function"
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        "(mathematical analysis) A meromorphic function which generalizes the notion of factorial to complex numbers and has singularities at the nonpositive integers; any of certain generalizations or analogues of said function, such as extend the factorial to domains other than the complex numbers."
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          "sense": "function which generalizes the notion of a factorial",
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          "word": "fonction gamma"
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          "code": "de",
          "lang": "German",
          "sense": "function which generalizes the notion of a factorial",
          "tags": [
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          ],
          "word": "Gammafunktion"
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        {
          "code": "hu",
          "lang": "Hungarian",
          "sense": "function which generalizes the notion of a factorial",
          "word": "gamma-függvény"
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        {
          "code": "it",
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        {
          "code": "it",
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          "sense": "function which generalizes the notion of a factorial",
          "tags": [
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          ],
          "word": "funzione Gamma di Eulero"
        },
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          "code": "ja",
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          "roman": "ganma kansū",
          "sense": "function which generalizes the notion of a factorial",
          "word": "ガンマ関数"
        },
        {
          "code": "fa",
          "lang": "Persian",
          "roman": "tâbe'-e gâmâ",
          "sense": "function which generalizes the notion of a factorial",
          "word": "تابع گاما"
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        {
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          "lang": "Polish",
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        },
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          "sense": "function which generalizes the notion of a factorial",
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        },
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          "code": "tr",
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          "sense": "function which generalizes the notion of a factorial",
          "word": "gama fonksiyonu"
        }
      ],
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        "Adrien-Marie Legendre",
        "American Mathematical Monthly",
        "Carl Friedrich Gauss",
        "Leonhard Euler"
      ]
    }
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  "word": "gamma function"
}

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  "etymology_text": "The function itself was initially defined as an integral (in modern representation, Γ(x)=∫₀ ᪲e⁻ᵗtˣ⁻¹dt) for positive real x by Swiss mathematician Leonhard Euler in 1730. The name derives from the notation, Γ(x), which was introduced by Adrien-Marie Legendre (1752—1833) (he referred to it, however, as the Eulerian integral of the second kind). Both Euler's integral and Legendre's notation shift the argument with respect to the factorial, so that for integer n>0, Γ(n) = (n−1)!. Carl Friedrich Gauss preferred π(x), with no shift, but Legendre's notation prevailed. Generalisation to non-integer negative and to complex numbers was achieved by analytic continuation.",
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      ],
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      "sense": "function that extends the domain of the factorial",
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    {
      "code": "fr",
      "lang": "French",
      "sense": "function which generalizes the notion of a factorial",
      "tags": [
        "feminine"
      ],
      "word": "fonction gamma"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "function which generalizes the notion of a factorial",
      "tags": [
        "feminine"
      ],
      "word": "Gammafunktion"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "function which generalizes the notion of a factorial",
      "word": "gamma-függvény"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "function which generalizes the notion of a factorial",
      "tags": [
        "feminine"
      ],
      "word": "funzione Gamma"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "function which generalizes the notion of a factorial",
      "tags": [
        "feminine"
      ],
      "word": "funzione Gamma di Eulero"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "roman": "ganma kansū",
      "sense": "function which generalizes the notion of a factorial",
      "word": "ガンマ関数"
    },
    {
      "code": "fa",
      "lang": "Persian",
      "roman": "tâbe'-e gâmâ",
      "sense": "function which generalizes the notion of a factorial",
      "word": "تابع گاما"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "function which generalizes the notion of a factorial",
      "tags": [
        "feminine"
      ],
      "word": "funkcja gamma"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "gámma-fúnkcija",
      "sense": "function which generalizes the notion of a factorial",
      "tags": [
        "feminine"
      ],
      "word": "га́мма-фу́нкция"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "function which generalizes the notion of a factorial",
      "tags": [
        "common-gender"
      ],
      "word": "gammafunktionen"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "function which generalizes the notion of a factorial",
      "tags": [
        "common-gender"
      ],
      "word": "Eulers gammafunktion"
    },
    {
      "code": "tr",
      "lang": "Turkish",
      "sense": "function which generalizes the notion of a factorial",
      "word": "gama fonksiyonu"
    }
  ],
  "word": "gamma function"
}

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