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I'm trying to solve an equation for B where

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

I plugged it into wolfram alpha and got:

enter image description here

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!)

J. M. ain't a mathematician
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corsiKa
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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? ( http://reference.wolfram.com/mathematica/ref/ProductLog.html ) – Myself Mar 01 '11 at 00:06
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    Lambert W function. http://mathworld.wolfram.com/LambertW-Function.html. –  Mar 01 '11 at 00:07
  • @Myself nope, it just mentions Z being integers. – corsiKa Mar 01 '11 at 00:10
  • @Sivaram are you saying that B is a set of values, not a particular solvable value? – corsiKa Mar 01 '11 at 00:10
  • @glowcoder: The value is negative of the Lambert W Function evaluated at $\frac{-1}{2e}$. –  Mar 01 '11 at 00:13
  • Actually this is a dupe: http://math.stackexchange.com/questions/10261/inverse-of-y-xex. +1 though, it would have been hard to find that out without knowing the name in the first place! – Aryabhata Mar 01 '11 at 00:19
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    There are two real solutions and infinite complex solutions. –  Mar 01 '11 at 00:19
  • @Moron - Perhaps in one sense, but the two questions are approached in a very different manner. – corsiKa Mar 01 '11 at 00:20
  • @glowcode: You are trying to invert $xe^{-x}$, so looks the same to me. Anyway, we need 4 more votes... – Aryabhata Mar 01 '11 at 00:23
  • @Moron that's merely the follow up. My REAL question is "What is W sub n" - the answer to that is, apparently, the Lambert W function. It would be like if I said "I want to reverse a string, and someone told me to use recursion. What is recursion?" and someone said "That's a duplicate of 'how to reverse a string'" The driving force behind the question is the terminology, not the math. – corsiKa Mar 01 '11 at 00:26
  • @glow: Don't agree with the analogy, but do agree that this is a terminology question and is technically not a dupe. – Aryabhata Mar 01 '11 at 00:30

1 Answers1

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

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

enter image description here

  • The text in that image is hardly readable on my browser... Why not just include a short writeup? +1 Anyway :-) – Aryabhata Mar 01 '11 at 00:13
  • @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 01 '11 at 00:15
  • @Moron: Added. I think the image will be better if you try opening the image on a new tab. –  Mar 01 '11 at 00:30
  • 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 01 '11 at 00:37