iterated exponential | tetration | tower of power

The power tower of order k is defined as a↑↑k congruent a^(a^(·^(·^(·^a)))) _︸_k, where ↑ is Knuth up-arrow notation, which in turn is defined by a↑^n k = a↑^(n - 1)[a↑^n(k - 1)] together with a↑k | = | a^k a↑^n 1 | = | a.

Ackermann function | exponential factorial | exponential function | Fermat number | Joyce sequence | Knuth up-arrow notation | Lambert W-function | Mills' constant | MRB constant | nested radical | omega constant | power | sophomore's dream | Steiner's problem