Question

I guess I'll go ahead and post my limit question here as well if anyone's interested:

http://math.stackexchange.com/questions/934005/limit-of-lambert-w-product-log-is-the-natural-log/

@ikram002p @BSwan @ganeshie8 @iambatman @dan815

Answer 1

I always thought Lambert w as a fake funciton lol, but the idea of taking the limit looks interesting xD

Answer 2

It's as real as any other function. What's the difference between ln(2) and W(2)? They're just numbers.

Answer 3

But yeah I can see why people would think it's fake, it's sort of a weird inverse that has a branch cut. It's just like how the inverse of x^2 is not a real function either, so we just take the real, positive part of it.

Answer 4

ikr, i never spent quality time messing with this function. x^2 and lnx are easy to understand for common people because we can relate them with familiar exponential functions or geometry. But the lamber W function is bit hard to comprehend - atleast for me. I know what it is and how to manipulate it, but thats it. Nothing more than that.

Answer 5

Since you have dropped a hint about L'hops, I would start something like below :

\[\large \lim_{n \rightarrow 0} n \cdot W\left( \frac{y^{1/n}}{n}\right)=\lim_{n \rightarrow 0} \dfrac{ W\left( \frac{y^{1/n}}{n}\right)}{1/n} \]

Answer 6

inverse functions reflected across the line y=x They just reverse the direction of what maps to what



You can show there is only one point, the global min, so there's only one branch cut if you look at the W(x) function. since for negative x values on the graph of y=xe^x you have only negative y values, it's pretty much just 1 to 1 except that one little part where it's multi valued.