Solve analytically an equation with Lambert function

Asked Aug 31 '16 at 16:15

Active Dec 17 '17 at 01:35

Viewed 209 times

Can this equation be solved analytically, maybe using Lambert $W$ function? $$(1-x)^{1-x}(1+x)^{1+x}=k$$

The problem is that I can't reformulate the equation in a way that lets me use Lambert's $W$ function: $f(x)e^{f(x)}$.

Thank you for your time and help!

edited Aug 31 '16 at 19:42

asked Aug 31 '16 at 16:15

Lorenzo

:/ I don't think you can get it into that form. – Simply Beautiful Art Sep 12 '16 at 00:01
$x^x = y$ can be inverted to $x = e^{W(\log y)}$. Maybe this can be used? – Hyperplane Dec 17 '17 at 02:06

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