Timeline for Invertibility of specific function
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2023 at 0:44 | comment | added | Тyma Gaidash | See inverse function discussion here or use inverse t function if it is allowed | |
| Oct 13, 2020 at 9:46 | history | edited | Costas Vlachos | CC BY-SA 4.0 |
Added some graphics, in order to better illustrate the problem. Also included a link to my accepted answer in Mathematics Stack Exchange.
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| Oct 11, 2020 at 22:03 | vote | accept | Costas Vlachos | ||
| Oct 9, 2020 at 15:07 | comment | added | Pietro Majer | I mean, the two are conjugated by translations, so invertibility in the large is the same problem (but local invertibility at $0$ is not, yes) | |
| Oct 9, 2020 at 13:24 | comment | added | მამუკა ჯიბლაძე | @PietroMajer There is a difference: $x-\sin x$ is $x^3/6+O(x^5)$ while $x+\sin x$ is $2x+O(x^3)$ | |
| Oct 9, 2020 at 4:14 | answer | added | Timothy Chow | timeline score: 13 | |
| Oct 9, 2020 at 1:36 | answer | added | Rob Corless | timeline score: 8 | |
| Oct 7, 2020 at 20:33 | comment | added | Timothy Chow | Related: When can an invertible function be inverted in closed form? | |
| Oct 7, 2020 at 18:24 | comment | added | Pietro Majer | Note that $$ 2(\varphi-\pi)- \sin (2(\varphi-\pi)) = -\frac{ 4\pi V\left(\varphi\right)^2}{A^2} $$ so what you should probably look for in the literature is the inverse of $u(x):=x\mapsto x-\sin x$ (Or equivalently $x\mapsto x+\sin x$). | |
| Oct 7, 2020 at 17:21 | answer | added | Iosif Pinelis | timeline score: 3 | |
| Oct 7, 2020 at 14:38 | comment | added | Costas Vlachos | @PiyushGrover, thanks for the comment. Yes, I am familiar with the Abel-Ruffini theorem, but I cannot see how it applies to my function, seeing that $V\left(\varphi\right)$ is not a polynomial of degree $n\geq5$. Please forgive me if the link between the Abel-Ruffini theorem and $V\left(\varphi\right)$ is obvious and I just don't see it, as I am not a mathematician. | |
| Oct 7, 2020 at 13:59 | comment | added | Piyush Grover | Are you familiar with en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem ? | |
| Oct 7, 2020 at 13:48 | review | Close votes | |||
| Oct 12, 2020 at 3:05 | |||||
| S Oct 7, 2020 at 13:39 | history | suggested | gmvh |
Added top-level tag and "closed-form-expressions" tag (since that's what the Q asks for)
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| Oct 7, 2020 at 13:33 | review | Suggested edits | |||
| S Oct 7, 2020 at 13:39 | |||||
| Oct 7, 2020 at 13:32 | review | First posts | |||
| Oct 7, 2020 at 14:36 | |||||
| Oct 7, 2020 at 13:27 | history | asked | Costas Vlachos | CC BY-SA 4.0 |