Timeline for Is the sequence of Apéry numbers a Stieltjes moment sequence?
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| Sep 3, 2014 at 19:16 | comment | added | Pietro Majer | Moreover, from this point of view, the boundary conditions in my answer should be sufficient to determine the solution $w$ just looking at the point $c$, arguing by exclusion, since as I showed a base of solutions is $u_1^2$ $u_1u_2$ and $u_2$ &cetera. | |
| Sep 3, 2014 at 19:05 | comment | added | Pietro Majer | Yes I think so, even with no numerics. Indeed I think I could turn the argument in my answer into a regularity result for the measure that solves the moment problem. Therefore, assuming Suvrit's existence proof, it follows that the measure whose moments are the Apéry numbers, does admit a density satisfying the third order EDO that I wrote. Thus, no wonder that the numerics suggest that there is such a solution. | |
| Sep 3, 2014 at 16:02 | comment | added | Gerald Edgar | I estimated the integral using 1000 points. It is between 751 and 824. From the asymptotic formula at OEIS, we see it should be $2^{5/4} c \pi^2 \approx 797.4$. I take this agreement as an indication I did this right. | |
| Sep 2, 2014 at 19:02 | history | edited | Gerald Edgar | CC BY-SA 3.0 |
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| Sep 2, 2014 at 18:54 | history | edited | Gerald Edgar | CC BY-SA 3.0 |
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| Sep 2, 2014 at 18:30 | history | edited | Gerald Edgar | CC BY-SA 3.0 |
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| Sep 2, 2014 at 2:44 | history | edited | Gerald Edgar | CC BY-SA 3.0 |
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| Sep 2, 2014 at 2:37 | history | edited | Gerald Edgar | CC BY-SA 3.0 |
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| Sep 2, 2014 at 2:00 | history | answered | Gerald Edgar | CC BY-SA 3.0 |