Category:Definitions/Taylor Series

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This category contains definitions related to Taylor Series.
Related results can be found in Category:Taylor Series.


Let $f$ be a real function which is smooth on the open interval $\openint a b$.

Let $\xi \in \openint a b$.


Then the Taylor series expansion of $f$ about the point $\xi$ is:

$\displaystyle \sum_{n \mathop = 0}^\infty \frac {\paren {x - \xi}^n} {n!} \map {f^{\paren n} } \xi$


It is not necessarily the case that this power series is convergent with sum $\map f x$.