# 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
show 6 more comments

## 1 Answer

$W(z)$ is the Lambert $W$ function.

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

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 The text in that image is hardly readable on my browser... Why not just include a short writeup? +1 Anyway :-) – Aryabhata Mar 1 '11 at 0:13 @Moron it was great for me when I clicked on the image to snap it to a better resolution. @Sivaram that's so weird, I can't get that output to come up. It would appear my result is .23 and 2.67 - Thank you so much! :) – corsiKa Mar 1 '11 at 0:15 @Moron: Added. I think the image will be better if you try opening the image on a new tab. – user17762 Mar 1 '11 at 0:30 What is a new tab? Just kidding :-) In any case, you need some supporting write up. I am pretty sure glowcoder could see the same thing before even creating this question :-) – Aryabhata Mar 1 '11 at 0:37