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How could one approximate Inverse Incomplete gamma function Г(s,x) by some simple analytical function f(s,Г)?
That means write something like x = f(s,Г) = 12*log(123.45*Г) + Г + 123.4^s .
(I need at least ideas or references.)
I’ve found out that x = f(s,Г) with given s can be nicely approximated by x = p0*(1-Г)^p1*ln(Г*p2). At least it worked for me with s <= 15 in region 0.001 < Г < 0.999.
Here p0,p1,p2 – is constants, which are chosen by approximation of f(s,Г) after you have chosen s.