Let $T \in S'(\mathbb{R}^n$) be a tempered distribution. I've seen a few resources (such as the first sentence of this Wikipedia article) refer to distributions being analytic or how one can analytically continue distributions. I'm familiar with the definitions for ordinary complex functions but not for distributions. Unfortunately the Wikipedia references a textbook that I do not have access to and I could not find a formal definition on the web.
How does one define analyticity for distributions and what does it mean to analytically continue a distribution? Also I've taken the distributions to be tempered as that's commonly done, but why is this required? Could we instead take a more general type of distribution, for example $\mathcal{D}'(\mathbb{R}^n)$?