# What is $W_n ?$

I'm trying to solve an equation for B where

$2 B e^{(1-B)}=1$

I plugged it into wolfram alpha and got:

What is that $W_n$ mean? How do I intrepret this answer?

(Feel free to retag it, I wasn't entirely sure what it falls under!)

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Isn't there a tiny box that says "W_k is the analytic continuation of the product log function" with a link to some documentation there? ( reference.wolfram.com/mathematica/ref/ProductLog.html ) –  Myself Mar 1 '11 at 0:06
Lambert W function. mathworld.wolfram.com/LambertW-Function.html. –  user17762 Mar 1 '11 at 0:07
@Myself nope, it just mentions Z being integers. –  corsiKa Mar 1 '11 at 0:10
@Sivaram are you saying that B is a set of values, not a particular solvable value? –  corsiKa Mar 1 '11 at 0:10
There are two real solutions and infinite complex solutions. –  user17762 Mar 1 '11 at 0:19

$W(z)$ is the Lambert $W$ function.
$W_k(-\frac{1}{2e})$ where $k \in \mathbb{Z}$ denotes the $k^{th}$ root of the equation $xe^x = -\frac{1}{2e}$