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taylor_s_formula [2013/09/16 10:45] nikolaj |
taylor_s_formula [2013/09/16 21:36] nikolaj |
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| | @#55EE55: $ R_k(x) = \sum_{|\alpha|=k+1} \frac{k+1}{\alpha !} \left( \int_0^1\ (1-s)^k\ F^{(\alpha)}(s\ x)\ \mathrm ds \right)\ x^\alpha $ | | | @#55EE55: $ R_k(x) = \sum_{|\alpha|=k+1} \frac{k+1}{\alpha !} \left( \int_0^1\ (1-s)^k\ F^{(\alpha)}(s\ x)\ \mathrm ds \right)\ x^\alpha $ | | ||
| - | where we use multi-index notation for $\alpha \in \mathrm{FinSequence}(\mathbb N)$, explained in [[Finite sequence]]. | + | where we use multi-index notation for $\alpha \in \mathrm{FinSequence}(\mathbb N)$, see [[Multi-index power]]. |
| ==== Discussion ==== | ==== Discussion ==== | ||
