Infinite towers & solutions to Lambert W-function - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Infinite towers & solutions to Lambert W-function (/showthread.php?tid=458) Infinite towers & solutions to Lambert W-function - brangelito - 06/16/2010 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? 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 = 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: $1=c^x x$