Perhaps it is obvious to some, but ( (x+1) / x ) ^ x converges to e.
And same for ( (x + 1) / x ) ^ (x+1).
Hence the identity x^y = y^x converges to e ^ e (or 15.154262241479264189760430272629911905528548536856139769140... via https://www.wolframalpha.com/input/?i=e+^+e )