See gamma function in All languages combined, or Wiktionary
{
"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": "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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"sense": "function which generalizes the notion of a factorial",
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"word": "funzione Gamma di Eulero"
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"sense": "function which generalizes the notion of a factorial",
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"sense": "function which generalizes the notion of a factorial",
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"word": "fonction gamma"
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"sense": "function which generalizes the notion of a factorial",
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"sense": "function which generalizes the notion of a factorial",
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"sense": "function which generalizes the notion of a factorial",
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"word": "funzione Gamma"
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"sense": "function which generalizes the notion of a factorial",
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"sense": "function which generalizes the notion of a factorial",
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"word": "га́мма-фу́нкция"
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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