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Here is an interesting math challenge

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Botsareus:
Rewrite the following equation in terms of A:


--- Quote ---A ^ A = B
--- End quote ---

A = ?

Numsgil:
You gotta use something called the Lambert W function.  It's an atomic operation, like trig functions and sqrt is, so your final answer will be in terms of it.  Something like: ln(B )/LambertW(ln(B ))

Botsareus:
Like I said, I can't read calculus, so I need the actual math as an equation.

For example: Let's say :

--- Quote ---LambertW(x) = x ^ x
--- End quote ---
Then I will need the whole thing to be written as:

--- Quote ---ln(B )/((ln(B )^ln(B ))
--- End quote ---

I am however impressed people know this stuff...

Numsgil:
It can't be done.  Just like sin(x) can't be expressed completely using other functions, neither can Lambert W.

If you want to approximate it, try its taylor series.

Botsareus:
A ^ A = B

I have no idea how to read a "Lagrange inversion theorem " too.

Numsgil or somebody, If you have time can you write vb code that solves: Rewrite the equation above terms of A.

As much as I do know the infinity sign means you can sum the calculations infinity. For my purposes a loop from 1 to 100 should be fine, If not at least I can change it later... Just specificity where this loop is in the code.

P.S.
I tried plugging "=LN(A2)/(LN(A2)-LN(A2)^2)" into Microsoft Exsel (A2 = B). It was not even close...

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