repeated exponents sign

Question

I'm wondering if there is a exponent version of $\sum$ or $\prod$ or I've even seen a big k used for repeated division. Is there a similar symbol for exponentiation and are there any useful mathematical identities or equations that make use of it. So for instance how could I show $x^{x/2^{x/4^{x/6^\dotsc}}}$

Answer 1

I've seen this operation represented as

$$ \underset{i=1}{\overset{n}{\LARGE\mathrm E}}\;x_i $$

Using this notation, your example would look something like this:

$$ \underset{i=1}{\overset{n}{\LARGE\mathrm E}}\;\frac{x}{2i} $$

Note that this is has a different first base than your example ($x$ vs. $\frac{x}{2}$) to simplify typesetting. You can get a little more detail on generic exponentiation on OEIS.

Tetration is a special case that has the form

$$ \underset{i=1}{\overset{n}{\LARGE\mathrm E}}\;a $$

You can get more details on tetration on Wikipedia.