Meanings
plural gamma functions
- mathematical analysisA 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.
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.
2 more examples
Chapter 3 deals with the p-adic gamma function.
1987, Kit Ming Yeung, Applications of p-adic gamma function to congruences of binomial coefficients, University of California, San Diego, page 3We 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.
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 167Synonyms: Euler integral of the second kind
Synonyms & antonyms
nounA 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.
Origin
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.
Full word history & related roots →Translations
Chinese Mandarin 伽馬函數 /伽马函数, Γ函數 /Γ函数
- 伽馬函數 /伽马函数function which generalizes the notion of a factorial
- Γ函數 /Γ函数 (gāmǎ hánshù)function which generalizes the notion of a factorial
French fonction gamma
- fonction gammafunction which generalizes the notion of a factorial
German Gammafunktion
- Gammafunktionfunction which generalizes the notion of a factorial
Hungarian gamma-függvény
- gamma-függvényfunction which generalizes the notion of a factorial
Italian funzione Gamma, funzione Gamma di Eulero
- funzione Gammafunction which generalizes the notion of a factorial
- funzione Gamma di Eulerofunction which generalizes the notion of a factorial
Japanese ガンマ関数
- ガンマ関数 (ganma kansū)function which generalizes the notion of a factorial
Persian تابع گاما
- تابع گاما (tâbe'-e gâmâ)function which generalizes the notion of a factorial
Polish funkcja gamma
- funkcja gammafunction which generalizes the notion of a factorial
Russian га́мма-фу́нкция
- га́мма-фу́нкция (gámma-fúnkcija)function which generalizes the notion of a factorial
Spanish función gamma
- función gammafunction which generalizes the notion of a factorial
Swedish gammafunktionen, Eulers gammafunktion
- gammafunktionenfunction which generalizes the notion of a factorial
- Eulers gammafunktionfunction which generalizes the notion of a factorial
Turkish gama fonksiyonu
- gama fonksiyonufunction which generalizes the notion of a factorial
Cite this entry
gamma function. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/gamma%20function
“gamma function.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/gamma%20function. Accessed November 2, 2026.
WatkinsX Dictionary, s.v. “gamma function,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/gamma%20function.
Source: gamma function on Wiktionary, CC BY-SA 4.0.