I am trying to understand Lambert W function. I am new to this special function. What is the actual meaning of the word two real branches of Lambert W function for any real $x$. How to find the branch point and branch cuts for the Lambert W function. When I used $lambertw(0,1)$ in Matlab i got the real value but for all other branches I got complex values. Actually I couldn't understand that why only these two branches gives real values. Can anyone can explain it clearly?

  • $\begingroup$ Did you look at en.wikipedia.org/wiki/Lambert_W_function ? $\endgroup$ – Claude Leibovici Dec 18 '14 at 7:47
  • $\begingroup$ Yes, I have seen that but things are not crystal clear to me. I didn't get the concept of branches, branch cut and branch point w.r.t Lambert W function. $\endgroup$ – user3563283 Dec 18 '14 at 9:20
  • $\begingroup$ Euler and Lambert showed that there is no real solution if $x < -\frac 1e$. The main branch is for $ -\frac 1e < x <\infty$, the other branch for $ -\frac 1e < x <0$. $\endgroup$ – Claude Leibovici Dec 18 '14 at 9:25
  • $\begingroup$ How the branch cuts of Lambert function are derived? $\endgroup$ – user3563283 Dec 23 '14 at 10:14

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