Timeline for For which $p>p^*$ does the inequality $\cos^2(−π/4+π/p)>1/2+π/p^2$ hold?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 9, 2023 at 15:45 | vote | accept | blockchain_dietmar | ||
| Nov 9, 2023 at 15:45 | vote | accept | blockchain_dietmar | ||
| Nov 9, 2023 at 15:45 | |||||
| Nov 6, 2023 at 23:12 | vote | accept | blockchain_dietmar | ||
| Nov 9, 2023 at 15:45 | |||||
| Nov 4, 2023 at 0:32 | comment | added | Тyma Gaidash | Would a series solution work? | |
| Nov 3, 2023 at 14:03 | history | edited | Emil Jeřábek | CC BY-SA 4.0 |
fix TeX
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| Nov 3, 2023 at 13:00 | comment | added | Toni Mhax | You may also write it as $\sin(\frac{2\pi}{p})>\frac{2\pi}{p^2}$ or $\sin(2\pi x)>2\pi x^2$, seeing their graphs could be clearer. | |
| Nov 3, 2023 at 12:22 | answer | added | Brendan McKay | timeline score: 1 | |
| Nov 3, 2023 at 12:05 | comment | added | Brendan McKay | Actually the derivative is not always positive. It becomes negative for $p>5.3$ approximately. Asymptotically the function is $\pi/p$. | |
| Nov 3, 2023 at 11:13 | review | Close votes | |||
| Nov 16, 2023 at 3:07 | |||||
| Nov 3, 2023 at 11:00 | comment | added | Daniel Weber | You can differentiate the difference, show it's positive for positive $p$, and solve $\cos^2(\pi(\frac1x-\frac14))=\frac12+\frac\pi{x^2}$ numerically. It doesn't seem like this root has a closed form. | |
| Nov 3, 2023 at 10:45 | history | edited | blockchain_dietmar | CC BY-SA 4.0 |
edited title
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| S Nov 3, 2023 at 10:43 | review | First questions | |||
| Nov 3, 2023 at 13:36 | |||||
| S Nov 3, 2023 at 10:43 | history | asked | blockchain_dietmar | CC BY-SA 4.0 |