Given that: $$ G(1) =\sum_{a=1}^{\infty} \frac{1}{a^{a}} $$
(this is just the Sophomore's dream series, but the rest are not)
$$ G(2) = \sum_{a=1}^{\infty} \sum_{b=1}^{\infty} \frac{1}{(ab)^{ab}} $$
$$ G(3) = \sum_{a=1}^{\infty} \sum_{b=1}^{\infty}\sum_{c=1}^{\infty} \frac{1}{(abc)^{abc}} $$
I'd like to interpolate $G(z)$ for $z\in\mathbb{C}$ (so that the result is analytic or meromorphic) given the above sequence. I can probably compute (with difficulty) $G(n)$ for many $n$.
- Does the sequence above specify a unique $G(z)$?
- Are there analytic tricks which would make finding such an interpolation easy? (the less I have to compute here, the better) *