Timeline for Positivity of sequences via generating series
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 23, 2010 at 1:12 | vote | accept | Wadim Zudilin | ||
| Jul 23, 2010 at 1:12 | history | bounty ended | Wadim Zudilin | ||
| Jul 22, 2010 at 5:09 | answer | added | Ryan Reich | timeline score: 3 | |
| Jul 19, 2010 at 23:35 | history | bounty started | Wadim Zudilin | ||
| Jul 17, 2010 at 22:06 | answer | added | Qiaochu Yuan | timeline score: 1 | |
| Jul 17, 2010 at 14:27 | comment | added | Wadim Zudilin | @Qiaochu: Thanks for pointing out to me the incorrectness of that part (this came from mixing two equivalent statements $A(x)\ge0$ and $A(xy)\ge0$). I now stay corrected. | |
| Jul 17, 2010 at 14:24 | history | edited | Wadim Zudilin | CC BY-SA 2.5 |
improved the text
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| Jul 16, 2010 at 17:37 | comment | added | Qiaochu Yuan | I am having trouble seeing how (*) follows from the double iteration of the false statement. Could you elaborate? | |
| Jul 16, 2010 at 2:25 | comment | added | Wadim Zudilin | Done! $ $ | |
| Jul 16, 2010 at 2:20 | history | edited | Wadim Zudilin | CC BY-SA 2.5 |
typos corrected; added 13 characters in body
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| Jul 16, 2010 at 2:05 | comment | added | Charles Staats | I agree with Will that the sentence "but it does not" is confusing and should be changed to "but it is not." | |
| Jul 16, 2010 at 1:37 | comment | added | Wadim Zudilin | Hi Will, yes I do (sometimes) positivity. :-) $( * )$ does follow by comparing the coefficients of $x^Ny^M$ when you fix successively $N=0,1,\dots$ and choose the corresponding $M$ sufficiently large. As for a 1-variable counterexample, take $A(x)=1+x-x^2+x^3$; then $A(x/(1-x))/(1-x)\ge0$. | |
| Jul 16, 2010 at 1:16 | comment | added | Will Jagy | Hi, Wadim. So you sometimes do "positivity" of series, same as the article I sent you. Let me be sure: (*) is true and really does follow from the expansion with the binomial coefficients? Then the next one with just $$ \left( \frac{x}{1-x} \right) $$ is false, so I suggest you switch to (But it is not!) Do you have an example of falsity for this one? | |
| Jul 16, 2010 at 0:47 | history | asked | Wadim Zudilin | CC BY-SA 2.5 |