Timeline for Integer-valued factorial ratios
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 17, 2021 at 2:49 | comment | added | Aaron Meyerowitz | So the $-1^n$ times the coefficient of $m^{m+n}$ in both $(x+1)^{2m}(x-1)^{2n}$ and $(1-4x)^{n-1/2}$. | |
| Oct 15, 2021 at 22:31 | comment | added | Ira Gessel | Incidentally, $(2m)!\,(2n)!/m!\,n!\,(m+n)!$ is the constant term in $(1+x)^m(1+1/x)^m(1-x)^n(1-1/x)^n$. | |
| Jul 30, 2010 at 23:38 | comment | added | Wadim Zudilin | With your very explicit idea in mind, I should ask Doron directly (he appeared on MO only once). I am not an expert on CT evaluations, although I know a huge database of some work in this direction, related to Calabi-Yau differential equations. | |
| Jul 30, 2010 at 17:22 | comment | added | Aaron Meyerowitz | I also don't know of any, and CT identities are not my area of expertise. On the other hand there are now known to be 3 2-parameter families and a 29 sporadic one parameter families (an! bn!)/(cn! dn! en!) there are a handful more sporadic families with 3 on the top 4 on the bottom and maybe 4 on top 5 on the bottom. SO it would not be totally amazing if root systems came in somehow. | |
| Jul 30, 2010 at 6:24 | comment | added | Wadim Zudilin | Welcome again, Aaron! That's a very good point, to interpret these factorial ratios as CTs... To my best knowledge there are no such things known for the 1-parametric families, but I might be wrong. +1 again and many thanks. | |
| Jul 30, 2010 at 6:04 | history | edited | Aaron Meyerowitz | CC BY-SA 2.5 |
again...
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| Jul 30, 2010 at 5:55 | history | answered | Aaron Meyerowitz | CC BY-SA 2.5 |