Timeline for The Bruss-Yor conjecture about an iterated integral
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Jul 29, 2012 at 19:16 | answer | added | fedja | timeline score: 9 | |
| Jul 16, 2012 at 15:18 | vote | accept | Jochen Wengenroth | ||
| Jul 16, 2012 at 15:18 | history | bounty ended | Jochen Wengenroth | ||
| Jul 12, 2012 at 18:33 | comment | added | juan | I just used Mathematica and the definition you give in this post. I give you here my definition, because certainly 100 is not the limit of my definition. And what I do not see in the numbers other can see. w[n_] := w[n] = Module[{Y, x, y, k}, Y = 1/(n + 1); Clear[x, y]; For[k = n - 1, k >= 1, k--, Y = (Y /. {x -> y}); (Print["Y = ", Y];) Y = Integrate[Y, {y, x, k/(k + 1)}]; (Print[k/(k+1)])]; n! (Y /. x -> 0) ] The last integral is also interesting when you do not compute it to 0. I do not saw your query before. | |
| Jul 12, 2012 at 16:39 | answer | added | Johan Wästlund | timeline score: 6 | |
| Jul 12, 2012 at 11:23 | history | bounty started | Jochen Wengenroth | ||
| Jul 3, 2012 at 7:26 | comment | added | Jochen Wengenroth | @juan: Thomas Bruss would like to ask you whether you have a kind of recursion to calculate the values up to $n=100$. This might be interesting for the general case. | |
| Jun 27, 2012 at 21:28 | comment | added | juan | I have checked (with Mathematica) until n=100. | |
| Jun 27, 2012 at 20:57 | comment | added | juan | The numbers do not appear to be a clue. Here are the first 1/2, 1/3, 5/16,19/60, 1687/5184, 2881/8640, 625961/1843200, 96314839/279936000, 302440148467/870912000000, 84408107137219/241416806400000, 2798993904047397389/7964120973312000000, 7033234035651624556939/19930212735713280000000 | |
| Jun 27, 2012 at 11:33 | history | edited | Jochen Wengenroth | CC BY-SA 3.0 |
added 12 characters in body
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| Jun 26, 2012 at 7:10 | comment | added | Jochen Wengenroth | Bruss and Yor checked the conjecture with Mathematica until $n=25$, here are the (rounded) values they report: $w_1=1/2$, $w_2=1/3$, $w_3=5/16$, $w_4=0.31667$, $w_5 = 0.32542$, $w_6 = 0.33345$, $\dots$ $w_{12} = 0.35289$, $\ldots$ $w_{25} = 0.36066$. | |
| Jun 26, 2012 at 3:28 | comment | added | Noam D. Elkies | What do the numerical values for the first "few" $n$ look like? | |
| Jun 25, 2012 at 14:43 | history | asked | Jochen Wengenroth | CC BY-SA 3.0 |