I'm aware of the following approximation that approaches the Lambert W Function: $$ W(f(x))\approx\ln\left(f(x)\right)-\ln\left(\ln(f(x))\right) $$ However, this approximation fails to capture the Lambert $W$ function if $f(x)$ is a decreasing function. Is there an approximation, potentially in terms of logs (though not necessarily) that approaches the same limit as the product log of a decreasing function? Thanks.
Asked
Active
Viewed 46 times
0
-
1There are various expansions here – Тyma Gaidash Jun 24 '23 at 23:43
-
1This approximation in fact works well if $f(x)$ tends to infinity as $x \to +\infty$. – Gary Jun 25 '23 at 06:54
-
In what range of $X$ do you want to approximate $W(X)$ ? – JJacquelin Jun 25 '23 at 07:16