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 Infinite towers & solutions to Lambert W-function brangelito Junior Fellow Posts: 2 Threads: 1 Joined: Jun 2010 06/16/2010, 02:32 PM (This post was last modified: 06/16/2010, 02:37 PM by brangelito.) The solution to the equation: Code:x*c^x -1 = 0Seems to be given by: Code:lim n->inf (1/c)^^nPut c=e, and you get the Lambert W-function. Is this already known? bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 06/16/2010, 02:50 PM (This post was last modified: 06/16/2010, 02:52 PM by bo198214.) (06/16/2010, 02:32 PM)brangelito Wrote: The solution to the equation: Code:x*c^x = 1Seems 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: $1=c^x x$ « Next Oldest | Next Newest »

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