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Questions regarding the Taylor series expansion of univariate and multivariate functions, including coefficients and bounds on remainders. A special case is also known as the Maclaurin series.

The Taylor expansion is the series expansion of a function at a point. It represents a function as an infinite sum with terms calculated from the functions derivatives at that point. It is defined as \begin{equation*} \sum^{\infty}_{n=0}\frac{f^{(n)}(a)}{n!}(x-a)^n=f(a)+\frac{f'(a)}{1!}(x-a)+\frac{f''(a)}{2!}(x-a)^2+\cdots \end{equation*}

It happens often that the Taylor expansion of $f$ at $a$ converges to $f$ on some neighborhood of $a$.

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