# Lambert W function

#### dwsmith

##### Well-known member
Based on Pickslides reference to the Lambert W function, I am now trying to solve this:

$$r = \frac{q\left(1-\exp\left\{-\frac{u^2}{\varepsilon}\right\}\right)}{u(q-u)}$$

So now I have this in the form $r = ue^u$ and I need to transform it to $u = w(r)$

I am not quite sure on how to do that though.

#### Sudharaka

##### Well-known member
MHB Math Helper
So now I have this in the form $r = ue^u$.....
Hi dwsmith,

Did you transform the original equation into the form $$X=Ye^{Y}$$ ? If so can we please see the result?

Kind Regards,
Sudharaka.