Math thread

[Notta]

Use this thread to talk about mathematics and its related fields.

 

[Notta]

For the expression x^y = y^x , there is of course the trivial solution of x=y, and if you graph it you will see the x=y line. However, there are other solutions. For x>e, this expression can be described by the function f(x) = -(x/ln(x)) * W(-x/ln(x)), where W(x) is the Lambert W-function. See picrel for an easier view of the function. The special thing about this expression is that for x<e, the function describing it is the inverse of the function describing it for x>e (i.e. f(x)). I've had some trouble with finding what the inverse of f(x) is, so any help would be very much appreciated

See this Desmos graph to try it out yourself: https://www.desmos.com/calculator/oocdrfovmb

 

[Notta]

BTW 1000th post in /off/