Inverse gamma function: Difference between revisions

Revision as of 18:22, 27 April 2023

Revision as of 18:22, 27 April 2023

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

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

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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(\alpha)=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