Timeline for Is the asymptotic expansion of this table of values $\log_{2}(x!)-.5$? If not, what is the expansion?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Sep 25, 2024 at 5:37 | history | edited | ydd | CC BY-SA 4.0 | Fixed an issue in the definition of `entropyAsymptotic2` |
| Sep 24, 2024 at 15:59 | comment | added | Daniel Lichtblau | As I note in my own response, integration only is good for the log and constant terms of the asymptotic approximation. So complexity notwithstanding, your method does better. | |
| Sep 23, 2024 at 17:38 | comment | added | ydd | @DanielLichtblau I look forward to seeing the answer. Note the IntegrateChangeVariables with t==Sqrt[-1+k] is for the exact summand. If you use asymSummand you can just integrate directly and the asymptotic entropy is very straightforward from there compared to my messy solution | |
| Sep 23, 2024 at 17:36 | comment | added | Daniel Lichtblau | I'll post it in a bit. Different methods can be useful to have in answers. | |
| Sep 23, 2024 at 17:05 | comment | added | ydd | @DanielLichtblau Ah yes, this does work! Especially if you IntegrateChangeVariables with t==Sqrt[-1+k] . I can add it to the answer if you want, but if you want to post it as your own answer that would be cool (since it was your idea). | |
| Sep 23, 2024 at 16:40 | comment | added | Daniel Lichtblau | Maybe a simpler path to the same result: replace the sum by an integral. Then justify that the difference is o(1) as r->infinity. (Roughly: denominator of each term ->0 while numerators change more slowly in r.) | |
| Sep 23, 2024 at 5:28 | comment | added | ydd | @A.Kato thank you | |
| Sep 23, 2024 at 4:50 | vote | accept | Arbuja | ||
| Sep 23, 2024 at 4:03 | history | edited | ydd | CC BY-SA 4.0 | added 177 characters in body |
| Sep 23, 2024 at 3:52 | history | edited | ydd | CC BY-SA 4.0 | added 192 characters in body |
| Sep 23, 2024 at 3:45 | history | edited | ydd | CC BY-SA 4.0 | Removed Abs from plot comparison of values that don't go to zero with r |
| Sep 23, 2024 at 3:42 | comment | added | A. Kato | (+1) Great answer like this again! | |
| Sep 23, 2024 at 3:35 | history | edited | ydd | CC BY-SA 4.0 | added 859 characters in body |
| Sep 23, 2024 at 3:09 | history | answered | ydd | CC BY-SA 4.0 |