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SovietWizard (talk | contribs) m Formula for the inverse gamma defined by the inverse Stirling's approximation was incorrect. It was originally positive 1/2 but it is not changed to be -1/2 to be accurate. Tags: Reverted Visual edit |
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The inverse gamma function also has the following [[asymptotic formula]]<ref>{{cite thesis |type=MS |last1=Amenyou |first1=Folitse Komla |last2=Jeffrey |first2=David |title="Properties and Computation of the inverse of the Gamma Function" |date=2018 |pages=28 |url=https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=7340&context=etd}}</ref>
<math display="block"> \Gamma^{-1}(x)\sim-\frac{1}{2}+\frac{\ln\left(\frac{x}{\sqrt{2\pi}}\right)}{W_{0}\left(e^{-1}\ln\left(\frac{x}{\sqrt{2\pi}}\right)\right)}\,,</math>
where <math>W_0(x)</math> is the [[Lambert W function]]. The formula is found by inverting the [[Stirling's approximation|Stirling approximation]], and so can also be expanded into an asymptotic series.
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