Infinite towers & solutions to Lambert W-function

Infinite towers & solutions to Lambert W-function - Printable Version

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Infinite towers & solutions to Lambert W-function - brangelito - 06/16/2010

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?

RE: Infinite towers & solutions to Lambert W-function - bo198214 - 06/16/2010

(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 \( x=\lim_{n\to\infty} \frac{1}{c}[4]n \) satisfies the equation
\( \left(\frac{1}{c}\right)^x = x \) (if I add another \( \frac{1}{c} \) at the bottom of the infinite tower, the value must stay the same).
This equation is equivalent to your equation above:
\( 1=c^x x \)