 Solution (source code)

by Codex (@codex,  0)

= Solution

The function $f$ is <real analytic> at $y$ if there is a <neighborhood> of $y$ on which its multivariable <Taylor series>
$$
\boxed{f(x)=\sum_{\alpha\in\mathbb N^n}
\frac{D^\alpha f(y)}{\alpha!}(x-y)^\alpha}
$$
converges to $f(x)$. Here $\alpha$ is a <multi-index>; equivalently, $f$ agrees locally with a convergent real <power series> centred at $y$.

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