Timeline for Estimate for an Airy integral
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 24, 2020 at 15:59 | comment | added | Giorgio Metafune | Similarly $\int_0^\infty f(t) \cos t\, dt \ge 0$ if $f \ge0$ is decreasing and convex. | |
| Aug 24, 2020 at 14:00 | comment | added | Bazin | Very nice, thanks for both answers. | |
| Aug 24, 2020 at 13:44 | comment | added | Fedor Petrov | yes, and may be done without change of variables (here this is a matter of taste, but when the change of variables is not so explicit, it looks more suitable), I posted the computation as an alternative answer | |
| Aug 24, 2020 at 13:33 | comment | added | Pietro Majer | so a double integration by parts, even better | |
| Aug 24, 2020 at 13:25 | comment | added | Fedor Petrov | alternatively, we may use $\sin \tau d\tau=d(1-\cos \tau)$ that yields $\int_0^\infty f(\tau)\sin \tau d\tau=-\int_0^\infty f'(\tau)(1-\cos \tau) d\tau\ge 0$ | |
| Aug 24, 2020 at 13:19 | history | answered | Pietro Majer | CC BY-SA 4.0 |