Revision as of 07:11, 3 April 2024 edit SovietWizard (talk \| contribs) 1 edit 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 ← Previous edit		Revision as of 10:37, 21 April 2024 edit undo 178.232.254.15 (talk) Undid revision 1217006437 by SovietWizard (talk). It should be +1/2 not -1/2, as otherwise it is the inverse factorial function, not inverse gamma. Tag: Undo Next edit →
Line 24: 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.

Inverse gamma function: Difference between revisions