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Infinite towers & solutions to Lambert W-function
#1
The solution to the equation:
Code:
x*c^x -1 = 0
Seems to be given by:
Code:
lim n->inf
(1/c)^^n
Put c=e, and you get the Lambert W-function.

Is this already known?
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#2
(06/16/2010, 02:32 PM)brangelito Wrote: The solution to the equation:
Code:
x*c^x = 1
Seems to be given by:
Code:
lim n->inf
(1/x)^^n

You mean 1/c instead of 1/x?!

The limit satisfies the equation
(if I add another at the bottom of the infinite tower, the value must stay the same).
This equation is equivalent to your equation above:
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