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 $y$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 105 / 3 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-105/3/a/solution