Timeline for Does the Apéry-like sequence $A_n=(n!)^2\sum_{k=0}^n { \rho \choose k}^2 { \rho+n-k \choose n-k}, \rho=e^{2 \pi i/3}$ change signs infinitely often?
Current License: CC BY-SA 4.0
22 events
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| Nov 12 at 8:35 | comment | added | Hjalmar Rosengren | I mean that the set of all zeroes of all the polynomials is dense. I wrote more details in an answer. | |
| Nov 12 at 8:31 | answer | added | Hjalmar Rosengren | timeline score: 2 | |
| Nov 11 at 22:52 | comment | added | CHUAKS | @Hjalmar Rosengren Can you explain how your observation applied. I am looking at the limits of the roots along fixed $k$. It is a discrete set, it cannot be dense. | |
| Nov 8 at 15:11 | comment | added | Hjalmar Rosengren | I see that you have updated your question based on my previous comment (which makes that comment look very silly). I believe the property you want follows from the fact that the orthogonality measure of the continuous dual Hahn polynomials is unique (the moment problem is determinate) and supported on the whole real line. For any such polynomials, the zeroes should be dense on the line. I haven't found a good reference for this but it should follow from the fact that, roughly speaking, the orthogonality measure can be recovered from the zeroes using Gauss quadrature. | |
| Nov 8 at 13:41 | history | edited | CHUAKS | CC BY-SA 4.0 |
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| Nov 8 at 0:53 | history | edited | CHUAKS | CC BY-SA 4.0 |
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| Nov 7 at 18:44 | history | edited | CHUAKS | CC BY-SA 4.0 |
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| Nov 4 at 7:25 | history | undeleted | CHUAKS | ||
| Nov 4 at 0:03 | history | deleted | CHUAKS | via Vote | |
| Nov 3 at 23:41 | history | undeleted | CHUAKS | ||
| Nov 3 at 23:40 | history | deleted | CHUAKS | via Vote | |
| Nov 3 at 20:52 | history | edited | LSpice | CC BY-SA 4.0 |
Apery -> Apéry
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| Nov 3 at 20:34 | comment | added | Hjalmar Rosengren | The polynomials $u_n$ are essentially continuous dual Hahn polynomials (with parameters $a=b=c=1/2$). Maybe some general facts about orthogonal polynomials, like interlacing of zeroes, can be useful. | |
| Nov 3 at 19:06 | history | edited | Somos | CC BY-SA 4.0 |
Simplify OEIS URL.
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| Nov 3 at 16:55 | history | edited | Eric Peterson |
no spectral sequences here
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| Nov 3 at 16:00 | history | undeleted | CHUAKS | ||
| Nov 3 at 15:51 | history | deleted | CHUAKS | via Vote | |
| Nov 3 at 15:36 | history | undeleted | CHUAKS | ||
| Nov 3 at 6:47 | history | deleted | CHUAKS | via Vote | |
| S Nov 3 at 3:19 | history | suggested | J. W. Tanner | CC BY-SA 4.0 |
corrected spelling in title
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| Nov 3 at 3:01 | review | Suggested edits | |||
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| Nov 2 at 21:46 | history | asked | CHUAKS | CC BY-SA 4.0 |