Looking for internet famous math prob on dist law.

[houlahound]

Can a table of values for W be computed?

ie

z in cloum a, W(z) in colum b.

 

[micromass]

Can a table of values for W be computed?

ie

z in cloum a, W(z) in colum b.

Yes, in exactly the same way that one can be computed for the log and the sin function.

 

[houlahound]

K, I will give the link a proper read, I stopped when it defined W as inverse branches of something else, what does that even mean.

 

[micromass]

It means that the $W$ function is an inverse function.
For example, $log(z) = w$ if and only if $e^w = z$. This means that the $\log$ is the inverse function of the exponential.

But situations like the log and the exponential aren't always this simple. Take $w =\sqrt{z}$. It is certainly true that $w^2 = z$, but $w$ isn't the only value for which $w^2 = z$, also $(-w)^2 = z$. So there are two solutions to $w^2 = z$. We choose one solution (namely the positive one) and call that $\sqrt{z}$. But we have made a quite arbitrary choice here, we could also take the negative. We say that the square root function has two branches (one for each choice). So there is a negative branch of numbers whose square is $z$ and a positive branch.

In the same way, there is no unique $w$ such that $we^w = z$. A choice must be made (in some case, in others there is a unique solution). These two choices define two "branches" of the W function.

 

[houlahound]

OK this I can do, expansion of W

This also

ETA

 

[micromass]

OK this I can do, expansion of W

This maybe

Yes, in the same way that the sin and the logarithm have such expansions! You see, there is little difference between the W and the logarithm. The only difference is that you've learned the log at a young age and thus are more "used" to it.

 

[houlahound]

But this discussion started that W can not be expressed by more elementary functions when from above clearly it can.

I have really enjoyed and value this discussion cos I got some new math. Appreciate you sticking with.

 

[micromass]

But this discussion started that W can not be expressed by more elementary functions when from above clearly it can.

The term elementary function is a technical term with a very specific meaning. You shouldn't put too much importance at these terms. A function being not-elementary doesn't mean it's hard to compute or anything.