Timeline for Showing that a family of polynomials has positive and real roots.
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jun 22, 2014 at 19:25 | history | suggested | Wolfgang | CC BY-SA 3.0 |
improved latex
|
| Jun 22, 2014 at 19:20 | review | Suggested edits | |||
| S Jun 22, 2014 at 19:25 | |||||
| Jan 23, 2013 at 21:22 | vote | accept | Enzo | ||
| Aug 1, 2012 at 3:43 | answer | added | matthias beck | timeline score: 5 | |
| Jul 17, 2012 at 18:34 | vote | accept | Enzo | ||
| Jan 23, 2013 at 21:22 | |||||
| Jul 17, 2012 at 18:31 | vote | accept | Enzo | ||
| Jul 17, 2012 at 18:32 | |||||
| Jul 17, 2012 at 12:37 | comment | added | Kevin O'Bryant | An early thing to try (although it doesn't work in this case) is to input the sequence of coefficients, (3,1,15,30,1,63,420,630 and 3,30,15,1,630 leaving off the first couple of terms and the signs, into the OEIS. Then, you might also try submitting them to superseeker, which you can learn about at the OEIS website (I haven't done this step with your sequence). If that doesn't work, you should then submit the sequence to the OEIS, so the next researcher doesn't start from scratch. | |
| Jul 17, 2012 at 1:05 | answer | added | Robert Israel | timeline score: 1 | |
| Jul 16, 2012 at 23:44 | answer | added | David E Speyer | timeline score: 16 | |
| Jul 16, 2012 at 23:43 | answer | added | john mangual | timeline score: 0 | |
| Jul 16, 2012 at 21:43 | comment | added | Enzo | Hi David, thanks for the comment. I have noticed that as well, and it reminded me the proof that the Hermite polynomial have real roots. Unfortunately, the same procedure does not seems to work here, since we have that the derivative is taken in $z$ and the roots are in $x$. | |
| Jul 16, 2012 at 20:40 | comment | added | David E Speyer | It appears that, furthermore, the roots of your polynomials are interlaced. For example, the roots of your quadratic are 2.37652, 12.6235; the roots of your cubic are 2.20173, 5.14109, 55.6572 and $2.20 < 2.37 < 5.14 < 12.6 < 55.6$. This suggests that there might be some sort of recursion relating the polynomials, as in Rolle's theorem or Sturm's theorem. | |
| Jul 16, 2012 at 20:24 | history | edited | Enzo | CC BY-SA 3.0 |
Added some details
|
| Jul 16, 2012 at 20:01 | history | edited | Enzo |
Add one more tag
|
|
| Jul 16, 2012 at 19:56 | history | asked | Enzo | CC BY-SA 3.0 |