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Dec 2, 2020 at 20:03 comment added R. N. Marley I don't care if the expression of the remainder is similar to the one-dimensional case. I just need to know if it is possible to obtain $f(x) - f(a) - \sum D^\alpha f(a) (y-a)^\alpha$ from $(*)$, in which case what would be the expression of the remainder?
Dec 2, 2020 at 16:57 comment added Abdelmalek Abdesselam I don't think you can. The integral remainder would need to involve several derivatives of order $m$ not just one given by the $\alpha$ you picked beforehand.
Dec 2, 2020 at 11:12 history asked R. N. Marley CC BY-SA 4.0