Timeline for Derivative formula
Current License: CC BY-SA 4.0
28 events
| when toggle format | what | by | license | comment | |
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| Nov 13, 2022 at 1:44 | answer | added | Tom Copeland | timeline score: 0 | |
| Nov 12, 2022 at 23:57 | history | edited | LSpice | CC BY-SA 4.0 |
Display displayed equation, while this is on the front page
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| Feb 21, 2017 at 21:04 | vote | accept | gurtonn | ||
| Feb 21, 2017 at 21:04 | vote | accept | gurtonn | ||
| Feb 21, 2017 at 21:04 | |||||
| Feb 15, 2017 at 20:38 | vote | accept | gurtonn | ||
| Feb 21, 2017 at 21:04 | |||||
| Feb 15, 2017 at 17:27 | comment | added | Deane Yang | Isn't it possible to derive this from Faà di Bruno's formula? | |
| Feb 15, 2017 at 13:49 | answer | added | Fedor Petrov | timeline score: 10 | |
| Feb 14, 2017 at 20:23 | answer | added | Ira Gessel | timeline score: 29 | |
| Feb 14, 2017 at 19:50 | comment | added | Ira Gessel | Yes, I will make it into an answer and add a few more details. | |
| Feb 14, 2017 at 19:40 | comment | added | Todd Trimble | @IraGessel That's great -- would you be able to make this into an answer, now that it's been reopened? | |
| Feb 14, 2017 at 19:06 | comment | added | Tom Copeland | Which paper of Cayley? | |
| Feb 14, 2017 at 19:03 | history | reopened |
Neil Strickland András Bátkai Ben Barber Ira Gessel Chris Godsil |
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| Feb 14, 2017 at 17:38 | comment | added | Ira Gessel | See Warren P. Johnson, The Pfaff/Cauchy derivative identities and Hurwitz type extensions, The Ramanujan Journal 13 (2007) pp. 167–201, link.springer.com/article/10.1007/s11139-006-0246-0, or my survey paper on Lagrange inversion, Journal of Combinatorial Theory, Series A 144 (2016) pp. 212–249, arxiv.org/abs/1609.05988, section 2.6. | |
| Feb 14, 2017 at 17:12 | comment | added | Richard Stanley | I also don't see why this was closed. | |
| Feb 14, 2017 at 16:21 | comment | added | Todd Trimble | @NeilStrickland I agree. I expect there would be a nice combinatorial interpretation as well. Do those who voted to close consider it obvious? It looks similar to a Leibniz product formula for higher derivatives, but I don't see how it follows trivially. | |
| Feb 14, 2017 at 15:52 | review | Reopen votes | |||
| Feb 14, 2017 at 19:03 | |||||
| Feb 14, 2017 at 15:40 | comment | added | Neil Strickland | I'm not sure why this was closed. Experiment with Maple shows that the formula holds when $k=9$ and $f$ is a polynomial of degree $10$, and this is big enough to convince me that it must be true in general. However, I do not see any obvious proof. | |
| Feb 14, 2017 at 14:57 | history | closed |
Gro-Tsen abx Wolfgang R.P. Marco Golla |
Not suitable for this site | |
| Feb 14, 2017 at 14:46 | comment | added | gurtonn | True, but I don't know how to do that for polynomials. | |
| Feb 14, 2017 at 14:30 | comment | added | Todd Trimble | Okay, what I'm trying to say is that we only have to look at the Taylor expansion (at a point $x_0$) of $f^k$ up to order $k$; higher terms can be disregarded to show equality at $x_0$. So I was suggesting just checking the identity at polynomials; that should be enough. | |
| Feb 14, 2017 at 14:18 | comment | added | gurtonn | why is it enough? the equation is not linear. | |
| Feb 14, 2017 at 14:17 | comment | added | Todd Trimble | Assuming it's true (I haven't checked), it ought to be enough just to prove it for powers $f(x) = x^n$. Have you checked it in that case? | |
| Feb 14, 2017 at 14:08 | comment | added | gurtonn | it should be true for any function (for simplicity lets say analytic) | |
| Feb 14, 2017 at 14:04 | comment | added | Ben McKay | Do you want to know which functions satisfy this equation for some $k$, or for all $k$, or something else? | |
| Feb 14, 2017 at 14:02 | review | Close votes | |||
| Feb 14, 2017 at 14:57 | |||||
| Feb 14, 2017 at 13:59 | history | edited | gurtonn | CC BY-SA 3.0 |
added 1 character in body
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| Feb 14, 2017 at 13:40 | review | First posts | |||
| Feb 14, 2017 at 13:45 | |||||
| Feb 14, 2017 at 13:39 | history | asked | gurtonn | CC BY-SA 3.0 |