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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.
Definition source: English Wiktionary via Wiktextract
Topics: mathematical-analysis, mathematics, sciences
Examples
- 2002, M. Aslam Chaudhry, Syed M. Zubair, On a Class of Incomplete Gamma Functions with Applications, Chapman & Hall / CRC Press, page 2, In particular, the exponential, circular, and hyperbolic functions are rational combinations of gamma functions.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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.
Across languages
Translations
15 source translations are retained for this English entry.
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Chinese Mandarin:
伽馬函數 /伽马函数
— function which generalizes the notion of a factorial
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Chinese Mandarin:
Γ函數 /Γ函数
(gāmǎ hánshù)
— function which generalizes the notion of a factorial
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French:
fonction gamma
— function which generalizes the notion of a factorial
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German:
Gammafunktion
— function which generalizes the notion of a factorial
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Hungarian:
gamma-függvény
— function which generalizes the notion of a factorial
-
Italian:
funzione Gamma
— function which generalizes the notion of a factorial
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Italian:
funzione Gamma di Eulero
— function which generalizes the notion of a factorial
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Japanese:
ガンマ関数
(ganma kansū)
— function which generalizes the notion of a factorial
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Persian:
تابع گاما
(tâbe'-e gâmâ)
— function which generalizes the notion of a factorial
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Polish:
funkcja gamma
— function which generalizes the notion of a factorial
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Russian:
га́мма-фу́нкция
(gámma-fúnkcija)
— function which generalizes the notion of a factorial
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Spanish:
función gamma
— function which generalizes the notion of a factorial
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Swedish:
gammafunktionen
— function which generalizes the notion of a factorial
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Swedish:
Eulers gammafunktion
— function which generalizes the notion of a factorial
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Turkish:
gama fonksiyonu
— function which generalizes the notion of a factorial
