There are the following common notations:
- Sums: $$\sum_{i=2}^4 i = 2 + 3 + 4 = 9$$
- Products: $$\prod_{i=2}^4 i = 2\times 3\times 4 = 24$$
Is there a (theoretical) one for:
- Exponentiation (conventional/top down) $$\ X_{i=2}^4 i = {2 ^ {3^4}} = 2^{81} =2\,417\,851\,639\,229\,258\,349\,412\,352$$
There is probably no need for of having a special notation for non-conventional Exponents (bottom up) like ${{2 ^ 3}^4} = 2 ^ {3\times4} = 4096$ in the first place. Since this is equivalent to $$n^{\prod_{i=n+1}^4 i} ;n=2$$
Or does this type of notation anyway only make sense for associative and commutative operations; or is this just too exotic?