Inverse gamma function: Difference between revisions

Revision as of 19:58, 27 April 2023

Revision as of 07:01, 3 May 2023

Line 2:

{{AFC submission|d|v|u=Onlineuser577215|ns=118|decliner=Majash2020|declinets=20230412023636|small=yes|ts=20221206210833}} <!-- Do not remove this line! -->

{{AFC comment|1=PleaseUsers fixon the referencesGamma tofunction page suggested that this. Theshould articlehave isits definitelyown notable,page mostlyinstead of being added as a new section on that page. See the referencestalk needpage toon be[[Gamma fixedfunction]]. [[User:Majash2020Onlineuser577215|Majash2020Onlineuser577215]] ([[User talk:Majash2020Onlineuser577215|talk]]) 028:3658, 123 AprilMay 2023 (UTC)}}

{{AFC comment|1=This article would fulfil notability for a mathematics article, except that the references to articles in the Proceedings of the American Mathematical Society give errors, and don't include date and DOI. See the instructions at [[Template:Cite journal]] and re-do those references. [[User:Newystats|Newystats]] ([[User talk:Newystats|talk]]) 10:11, 19 March 2023 (UTC)}}

----

{{Distinguish|Inverse-gamma distribution|Reciprocal gamma function}}

{{Short description|Inverse of the gamma function}}

{{Draft topics|mathematics}}

{{AfC topic|stem}}

In [[mathematics]], the inverse gamma function <math>\Gamma^{-1}(x)</math> is the [[inverse function]] of the [[gamma function]]. In other words, it is the function satisfying <math display="inline">\Gamma(y)=x</math>. For example, <math>\Gamma^{-1}(24)=5</math> <ref>{{Cite journal |last=Borwein, Corless |title=Gamma and Factorial in the Monthly |journal=|year=2017 |arxiv=1703.05349 }}</ref>. Usually, the inverse gamma function refers to the principal branch on the interval <math>\left(\Gamma(\alpha)= 0.8856031..., \infty\right)</math> where <math>\alpha=1.4616321...</math> is the unique positive number such that the [[digamma function]] <math>\Psi(\alphax)=0</math> <ref>{{cite journal |last1=Uchiyama |first1=MITSURU |title=The principal inverse of the gamma function |date=April 2012 |url= https://www.jstor.org/stable/41505586 |journal=Proceedings of the American Mathematical Society|volume=140 |issue=4 |pages=1347 |doi= 10.1090/S0002-9939-2011-11023-2

|jstor=41505586 |s2cid=85549521 |access-date=20 March 2023}}</ref>. where <math>\Psi(x)</math> is the [[digamma function]].

==== Definition ====