Timeline for Is $ \sum\limits_{n=0}^\infty x^n / \sqrt{n!} $ positive?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 13, 2016 at 20:02 | comment | added | Andreas Rüdinger | @David Speyer: I'm wondering if the cancellation is more amazing / surprising than the cancellation that happens for the power series for $\exp(x)$ for large negative values of x. | |
| S Jul 15, 2013 at 7:28 | history | suggested | Thomas Klimpel | CC BY-SA 3.0 |
fixed latex rendering, after wondering why it didn't work
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| Jul 15, 2013 at 7:23 | review | Suggested edits | |||
| S Jul 15, 2013 at 7:28 | |||||
| Jan 6, 2012 at 1:50 | comment | added | J Russell | Gottfried, thank you for the numerical evaluation. This is consistent with how I believe the series behaves and with the numerical calculations I have done, although I didn't have the tools to push it out anywhere near as far as you did. A comment and an open-ended question: Presumably one could use interval arithmetic to produce a computer-aided proof of positivity for some negative values of $x$. Suppose you could prove positivity down to some large negative value. How large in magnitude would that $x$ have to be for you to really believe, absent a proof, that the series is positive? | |
| Jan 6, 2012 at 0:57 | comment | added | Liviu Nicolaescu | This function is indeed miraculous. | |
| Jan 6, 2012 at 0:23 | comment | added | David E Speyer | Note again the amazing cancellation. To compute that −70 term, the largest term in the sum is $(70)^{70^2}/\sqrt{(70)^2!} \approx e^{70^2/2}$. | |
| Jan 6, 2012 at 0:13 | comment | added | Liviu Nicolaescu | Thanks for the table. After I wrote that there is a minimum I did some additional computations and I realized I was wrong. Your table suggests that the question is far form trivial. | |
| Jan 5, 2012 at 22:29 | history | answered | Gottfried Helms | CC BY-SA 3.0 |