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DOUBLE PRECISION FUNCTION LAMBERTW(X) - Lambert W-function




In this routine the Lambert W-function ${\rm LAMBERTW(X)}=W(x)$, i.e. the solution of

\begin{displaymath}
W(x)\exp(W(x))=x
\end{displaymath} (1)

is calculated.

The following simple, but accurate approximation is used:

\begin{displaymath}
W(x)\approx \left\{
\begin{array}{l@{\quad:\quad}l}
0.665\cd...
...{1}{\ln(x)})\cdot\ln(\ln(x)) & x > 500\,.
\end{array} \right.
\end{displaymath} (2)



A. Ringwald and F. Schrempp

1999-08-21