I'm basing this question on some asumptions: first, that there are multiple "places" where one can "do" analysis (such as $\mathbb{R}$,\mathbb{C}, $p$-adic numbers, maybe Banach/Hilbert spaces) and second, that it is possible to define holomorphic and analytic functions.
In every such place (what would a precise definition be?) it is expected that analytic$\Rightarrow$holomorphic, so when and where is the converse true? If we are working in $\mathbb{C}$ we can, so what makes it special?
Sorry for the very non-rigorous question, hopefully it is understood what king of answer I expect
Thanks!