Timeline for Polynomials for which $f''$ divides $f$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2018 at 15:35 | answer | added | David E Speyer | timeline score: 15 | |
| Feb 11, 2018 at 14:46 | comment | added | David E Speyer | @Nemo feel free to post an answer stating this if you'd like the points. en.wikipedia.org/wiki/Gegenbauer_polynomials at $\alpha = -1/2$ is exactly what I want. | |
| Feb 11, 2018 at 14:40 | comment | added | David E Speyer | Thanks! This special case is basically the general case: If $f''$ divides $f$ then $(f \circ \ell)''$ divides $f \circ \ell$ for any affine linear transformation $\ell$, so we can put $a$ and $b$ anywhere we want. I left them unspecified because I wasn't sure what normalization previous researchers would have used. It looks like, indeed, these Gegenbauer polynomials are what I want, with the normalization that the leading terms are $x^n-x^{n-2} + \cdots$. | |
| Feb 11, 2018 at 14:32 | comment | added | Nemo | Particular case is studied in this paper Kostov, "Interlacing properties and the Schur-Szeg\H {o} composition", page 8, and they are called Gegenbauer and Narayana polynomials. | |
| Feb 11, 2018 at 14:25 | history | edited | David E Speyer | CC BY-SA 3.0 |
added 489 characters in body
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| Feb 11, 2018 at 14:05 | history | asked | David E Speyer | CC BY-SA 3.0 |