Timeline for Why does Mathematica report that $\int_1^\infty\frac{\sin(\sqrt{x})}{\sqrt{x}}dx$ = $2\cos(1)$?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 11, 2018 at 4:26 | vote | accept | JEM | ||
| Apr 13, 2017 at 12:55 | history | edited | CommunityBot |
replaced http://mathematica.stackexchange.com/ with https://mathematica.stackexchange.com/
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| Mar 5, 2016 at 12:18 | history | edited | Michael E2 | CC BY-SA 3.0 |
Added omission
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| Feb 22, 2016 at 1:35 | history | bounty ended | Vadim Ponomarenko | ||
| Feb 21, 2016 at 3:50 | history | edited | Michael E2 | CC BY-SA 3.0 |
Added bug info
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| Feb 21, 2016 at 2:37 | comment | added | Michael E2 | @J.M. Probably most regularizations will give the same answer. Don't know why Abel didn't occur to me first. I actually use that from time to time. (Thank for the spelling correction.) | |
| Feb 21, 2016 at 2:22 | comment | added | J. M.'s missing motivation♦ |
Apart from Cesàro summability, one could also consider Abel summability for this formally divergent integral, in which case you also obtain the result $2\cos 1$: Limit[Integrate[Exp[-c x] Sinc[Sqrt[x]], {x, 1, ∞}, GenerateConditions -> False], c -> 0, Direction -> -1] // FullSimplify
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| Feb 21, 2016 at 2:18 | history | edited | J. M.'s missing motivation♦ | CC BY-SA 3.0 |
edited body
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| Feb 21, 2016 at 2:02 | history | answered | Michael E2 | CC BY-SA 3.0 |