Timeline for Is the solution to this trig function known to be algebraic or transcendental?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2021 at 0:53 | vote | accept | Mitch | ||
| Mar 2, 2021 at 20:06 | answer | added | Timothy Chow | timeline score: 4 | |
| Mar 2, 2021 at 4:57 | comment | added | Timothy Chow | @GerryMyerson Can't we take $l=1$, $n=4$, trig$_1 = \sin$, $\theta_1(x) = 2/(x+1)$, trig$_2 = \cos$, $\theta_2(x) = 2/x$, trig$_3 = \sin$, $\theta_3(x)=2/x$, trig$_4=\cos$, $\theta_4(x) = 2/(x+1)$, and $R(A,B,C,D,E) = A^2\cdot B \cdot(3 + 2C) - (A+1)^2\cdot D \cdot(3+2E)$? | |
| Mar 2, 2021 at 4:07 | comment | added | Gerry Myerson | @Tim, I don't think OP's equation meets the Conway-Jones definition of a trigonometric Diophantine equation. | |
| Mar 2, 2021 at 1:56 | comment | added | Timothy Chow | It may at least be possible to show that $x$ is irrational. Conway and Jones gave an algorithm for transforming a trigonometric Diophantine equation into an ordinary Diophantine equation. So one could try running their algorithm on your equation for $x$, and with luck, one might be able to show that the resulting Diophantine equation has no rational solutions. | |
| Mar 1, 2021 at 16:57 | history | edited | Mitch | CC BY-SA 4.0 |
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| Mar 1, 2021 at 7:24 | comment | added | Michael Engelhardt | Mathematica to 100 digits yields 2.139212753707616852225181645744445960113284555577699941769231477262384484929696716416193938704042851 | |
| Mar 1, 2021 at 7:04 | comment | added | markvs | You should try Mathematica, Maple or Matlab. | |
| Mar 1, 2021 at 5:45 | history | edited | Mitch | CC BY-SA 4.0 |
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| Mar 1, 2021 at 4:44 | history | asked | Mitch | CC BY-SA 4.0 |