Timeline for how to evaluate the following double summation to infinity without using integration method?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 17, 2015 at 14:56 | comment | added | Igor Rivin | @NoamD.Elkies Yes, indeed Mathematica is happy to evaluate it, but it would be interesting if there were a closed form (of course, it depends on what you mean by "closed"). | |
| May 17, 2015 at 1:39 | comment | added | Noam D. Elkies | The sum converges fast enough to be computed efficiently to any desired accuracy as it stands. But I suspect that there might be no closed form. | |
| May 17, 2015 at 0:00 | comment | added | Igor Rivin | @WillSawin agreed on both points. I fixed the first, not the second, since it still doesn't actually give any sort of closed form for the sum. | |
| May 16, 2015 at 23:58 | history | edited | Igor Rivin | CC BY-SA 3.0 |
fixed bug pointed out by Will.
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| May 16, 2015 at 23:56 | comment | added | Will Sawin | In your notation the area of a circle is $\pi r$. The sum you get with the aporoximation can be computed exactly by summation by parts again. | |
| May 16, 2015 at 19:41 | history | answered | Igor Rivin | CC BY-SA 3.0 |