Timeline for Is formula valid for relating $\pi$ with ALL of its OEIS A002485(n)/A002486(n) convergents?
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| Aug 6, 2023 at 16:11 | comment | added | Alex | @GerryMyerson Both answers unfortunately don't provide the proof (or disproof) that for each given "n" the number of parameters could be reduced from four {i,j,k,l}. Obviously the practical method of such reducing isn't provided either. | |
| Aug 5, 2023 at 22:39 | comment | added | Alex | @GerryMyerson Ute Hahn proof is constructive because in the part 2 it shows how to obtain at least one pair of specific values for "i" and "k" for each given value of "n". Will's answer only proves that such pairs exist. Please note that before obtaining specific values for "i" and "k" for each given value of "n" required brute trial and error algorithm. | |
| Aug 5, 2023 at 22:05 | comment | added | Gerry Myerson | I think by the definitions you give, Will's answer is constructive. Leaving details to the reader doesn't make an answer nonconstructive. If I write, "You calculate $3(4+5)$ by first adding $4$ and $5$ and then multiplying the result by $3$," that's constructive even though I didn't include the information that $4+5=9$ and $3\times9=27$. | |
| Aug 5, 2023 at 14:13 | comment | added | Alex | @GerryMyerson You seems to be don't understand what is constructive proof. A constructive proof is a method of mathematical proof that not only demonstrates the existence of a certain mathematical object but also provides a clear and specific procedure for constructing or finding that object. This approach shows not only that something exists but how to create or identify it. It's often used in fields like number theory and computer science to establish the existence of solutions or algorithms. | |
| Aug 5, 2023 at 6:14 | comment | added | Gerry Myerson | What's nonconstructive about Will's answer? | |
| Aug 5, 2023 at 0:46 | comment | added | Alex | @GerryMyerson - I prefer constructive proof given by Ute Hahn. | |
| Aug 4, 2023 at 21:51 | comment | added | Gerry Myerson | Do you have anything to say, Alex, about the answer @Will Sawin posted in July 2017? | |
| Jun 21, 2023 at 14:13 | history | edited | Alex | CC BY-SA 4.0 |
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| Jun 21, 2023 at 12:02 | history | edited | Alex | CC BY-SA 4.0 |
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| May 12, 2023 at 11:28 | history | edited | Alex | CC BY-SA 4.0 |
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| Jul 16, 2017 at 15:17 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 13, 2017 at 3:57 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 13, 2017 at 3:15 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 4, 2017 at 20:56 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 4, 2017 at 14:43 | answer | added | Will Sawin | timeline score: 10 | |
| Jul 4, 2017 at 14:02 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 4, 2017 at 13:14 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 1, 2017 at 2:59 | answer | added | Alex | timeline score: 0 | |
| Apr 17, 2017 at 22:31 | comment | added | Alex | The 1st, 2nd ad 5th formulas (counting from the top down) found by Jaume Oliver Lafont in oeis.org/wiki/User:Jaume_Oliver_Lafont/Dalzell-type_integrals are covered by my suggested parametrical formula: for the 1st {i, j, k, l} = {-1, 0, 1, 4} for the 2nd {i, j, k, l} = {-1, -1, 1, 1} for the 5th {i, j, k, l} = {-1, 1, 1, 5} Alas the 3rd, 4th and the 6th formulas and Jaume's formula for pi-333/106 in math.stackexchange.com/questions/1956/… are NOT covered by suggested parametrical formula, | |
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Mar 25, 2017 at 1:17 | history | edited | Alex | CC BY-SA 3.0 |
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| Mar 24, 2017 at 22:37 | comment | added | Alex | see Randall's answer at math.stackexchange.com/a/2198869/28343 | |
| Feb 12, 2016 at 19:55 | history | edited | Alex | CC BY-SA 3.0 |
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| Feb 12, 2016 at 15:06 | history | edited | Alex | CC BY-SA 3.0 |
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| Feb 12, 2016 at 14:10 | history | edited | Alex | CC BY-SA 3.0 |
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| S Feb 11, 2016 at 16:53 | history | bounty ended | CommunityBot | ||
| S Feb 11, 2016 at 16:53 | history | notice removed | CommunityBot | ||
| Feb 6, 2016 at 19:51 | history | edited | Alex | CC BY-SA 3.0 |
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| S Feb 3, 2016 at 15:23 | history | bounty started | Alex | ||
| S Feb 3, 2016 at 15:23 | history | notice added | Alex | Canonical answer required | |
| Feb 3, 2016 at 15:16 | history | edited | Alex | CC BY-SA 3.0 |
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| Feb 3, 2016 at 14:41 | history | edited | Alex | CC BY-SA 3.0 |
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| Feb 1, 2016 at 23:51 | history | edited | Alex | CC BY-SA 3.0 |
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| Feb 1, 2016 at 14:00 | history | edited | Alex | CC BY-SA 3.0 |
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| Jan 31, 2016 at 17:21 | comment | added | Alex | @Sylvain JULIEN - I don't know. | |
| Jan 31, 2016 at 11:11 | comment | added | Sylvain JULIEN | Is it related to the fact that $\pi$ is a degree $2$ period? | |
| Jan 31, 2016 at 4:37 | history | edited | Alex | CC BY-SA 3.0 |
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| Jan 30, 2016 at 22:51 | comment | added | Alex | @Federico Poloni - here I am asking to provide analytical analysis/proof, while there I am asking re computational aspects of the issue. | |
| Jan 30, 2016 at 20:02 | comment | added | Federico Poloni | OP asked something very similar also on scicomp.stackexchange: scicomp.stackexchange.com/questions/21918/… | |
| Jan 30, 2016 at 19:48 | history | edited | Alex | CC BY-SA 3.0 |
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| Jan 17, 2016 at 22:32 | history | edited | Alex | CC BY-SA 3.0 |
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| Jan 11, 2016 at 21:56 | history | edited | GH from MO |
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| Jan 11, 2016 at 21:48 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 24, 2014 at 9:20 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 24, 2014 at 9:11 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 24, 2014 at 8:40 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 24, 2014 at 7:06 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
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| Jul 24, 2014 at 3:18 | comment | added | Gerry Myerson | OK. Another tip, then; @(xxx) doesn't notify xxx; it has to be @xxx to notify xxx that you have made a comment directed to that person. | |
| Jul 24, 2014 at 2:26 | comment | added | Alex | @(Gerry Myerson) - I will try to learn but for this particularly recently added content (which reflects on Matt B's contribution) - the stuff to the right of the arrow sign - is actual Maple code, which you could copy (while in the "edit" mode) and then paste into (let say) Inverse Symbolic Calculator (it accepts Maple code) and run it there. | |
| Jul 24, 2014 at 2:05 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 24, 2014 at 1:02 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 24, 2014 at 0:52 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 24, 2014 at 0:45 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 24, 2014 at 0:41 | comment | added | Gerry Myerson | May I suggest, Alex, that you learn something about formatting mathematics on this site, as your latest edit is unreadable. Have a look at how the earlier parts of your question are formatted, and/or click on the "help" link on this page. | |
| Jul 23, 2014 at 16:51 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 13, 2014 at 4:36 | comment | added | Lucia | Also posted at MSE: math.stackexchange.com/questions/860499/… | |
| Jul 13, 2014 at 4:03 | review | First posts | |||
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| Jul 13, 2014 at 1:07 | comment | added | Gerry Myerson | @Kirill, $x^{\ell}(1-x)^m=(1+x^2)p(x)+ax+b$; now evaluate at $x=i$, and note that $1-i=\sqrt2e^{-i\pi/4}$. | |
| Jul 12, 2014 at 17:58 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 12, 2014 at 14:03 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 10, 2014 at 19:53 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 10, 2014 at 18:54 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 10, 2014 at 18:20 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 10, 2014 at 17:45 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 10, 2014 at 17:12 | history | edited | Alex | CC BY-SA 3.0 |
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| Jul 10, 2014 at 14:40 | comment | added | Kirill | It does appear, though, that $x^l(1-x)^m\bmod 1+x^2$ has always zero or a power of two as its constant coefficient. | |
| Jul 10, 2014 at 14:34 | comment | added | Kirill | The integral $I_{l,m}=\int_0^1 \frac{x^l(1-x)^m}{1+x^2}\,dx$ is always a linear combination of $1$, $\pi$, and $\log 2$ with rational coefficients. So you can always find $k$ and $i+k$ so that $k I_{l,m}+(i+k)I_{l+2,m}$ is $\alpha+\beta\pi$. I'm not sure how you prove that $\beta/i$ is a power of two, though. | |
| S Jul 10, 2014 at 14:28 | history | suggested | CommunityBot | CC BY-SA 3.0 |
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| Jul 10, 2014 at 13:58 | comment | added | j.c. | Possibly somewhat related: mathoverflow.net/questions/67384/… | |
| Jul 10, 2014 at 13:10 | history | asked | Alex | CC BY-SA 3.0 |