Simple approximation of Inverse Incomplete gamma function

Question

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.)

Answer 1

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.