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Talk:Cauchy formula for repeated integration

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This is an old revision of this page, as edited by Sniffnoy (talk | contribs) at 17:23, 28 July 2011. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

This entire page needs a lot of work, particularly in the scalar "proof" section. KlappCK (talk) 17:49, 27 July 2011 (UTC)[reply]

Well, that's overstating things a bit. Is there a lot to say about the Cauchy formula for repeated integration? :P I can fill in the rest of the proof sometime today, but it's a straightforward application of the multidimensional chain rule. Hell, I'll put that much in right now, that takes no work... Sniffnoy (talk) 06:31, 28 July 2011 (UTC)[reply]
Huh, now that I look closer, it's worse than I realized -- it pretty much totally ignores basepoint issues, concerning itself solely with the antiderivative part of the result. OK, I'll fix that later. Sniffnoy (talk) —Preceding undated comment added 06:37, 28 July 2011 (UTC).[reply]
Agreed Sniffnoy, I will give you another 48 hours to improve upon this (arguably) more elegant proof by induction before I go in and simply demonstrate that the result (Cauchy's formula) is correct by working "backwards" via repeated differentiation. I think that this section would also benefit from a rigorous explanation of when this rule applies. KlappCK (talk) 12:49, 28 July 2011 (UTC)[reply]
Uh... how does that differ from the approach currently there? I'm not following. This *is* a proof by repeated differentiation. Sniffnoy (talk) 17:23, 28 July 2011 (UTC)[reply]
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