Timeline for Sum of 'the first k' binomial coefficients for fixed $N$
Current License: CC BY-SA 4.0
26 events
| when toggle format | what | by | license | comment | |
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| May 13, 2022 at 13:43 | answer | added | jlewk | timeline score: 0 | |
| May 12, 2022 at 18:56 | history | edited | kodlu | CC BY-SA 4.0 |
edited title
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| May 12, 2022 at 17:20 | answer | added | Max Alekseyev | timeline score: 0 | |
| Aug 21, 2021 at 14:24 | answer | added | Pietro Majer | timeline score: 3 | |
| Apr 6, 2021 at 10:38 | answer | added | Vili | timeline score: 0 | |
| May 2, 2019 at 19:49 | comment | added | Dmitry Vaintrob | *Sorry, thinking about it some more, both cases will give something rapidly oscillating. If you split up the integrand into a radial and polar part, it should not be too difficult to compute using some standard oscillating integral techniques | |
| May 2, 2019 at 19:31 | comment | added | Dmitry Vaintrob | You are interested in the dot product of the Fourier series $A(x) = \sum_{j\ge -k} e^{j(ix)}$ and $B(x) = \sum_{j=0}^n \binom{n}{j} e^{j(ix)}.$ There are nice closed forms for both functions, though of course $A(x)$ is singular and should be treated carefully (for example by fudging it and studying $A(x-i\epsilon)$ to get a smooth Fourier series.) The resulting integral will be dominated by its contribution near $x=0;$ depending on $k<<\sqrt{n}$ or $k>>\sqrt{n}$ it will either be a simple or an oscilating integral. | |
| Sep 20, 2018 at 8:40 | history | edited | YCor | CC BY-SA 4.0 |
added symbol $f$ used throughout the answers
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| Sep 18, 2018 at 6:35 | answer | added | Erel Segal-Halevi | timeline score: 1 | |
| Sep 18, 2018 at 6:21 | comment | added | Erel Segal-Halevi | See also here: math.stackexchange.com/q/1610438/29780 | |
| Aug 14, 2018 at 9:25 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added the (binomial-coefficients) tag - the question has been bumped anyway
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| Oct 1, 2017 at 9:45 | comment | added | Peter Heinig | Just to add one more $\varepsilon$ of relevant context and interconnectedness: the newest example of these quantities being put to use is Zur Luria's answer to this MO question, given one hour ago. A dictionary 'here:there' is '$i$ : $i$' , '$k$ : $n-1$' , '$0$ : $1$' , ' $N$ : $c$ ' . | |
| Nov 11, 2015 at 13:38 | answer | added | Brendan McKay | timeline score: 15 | |
| Jun 10, 2015 at 19:09 | answer | added | Matt | timeline score: 8 | |
| Jun 30, 2011 at 15:58 | answer | added | Barry Cipra | timeline score: 8 | |
| Aug 31, 2010 at 21:37 | answer | added | Yaroslav Bulatov | timeline score: 37 | |
| Mar 6, 2010 at 3:24 | answer | added | Douglas Zare | timeline score: 11 | |
| Mar 6, 2010 at 2:30 | answer | added | Douglas Zare | timeline score: 19 | |
| Mar 5, 2010 at 23:55 | vote | accept | mathy | ||
| Mar 5, 2010 at 22:35 | answer | added | Michael Lugo | timeline score: 78 | |
| Mar 5, 2010 at 22:03 | answer | added | Alex R. | timeline score: 7 | |
| Mar 5, 2010 at 20:43 | answer | added | Justin Melvin | timeline score: 15 | |
| Mar 5, 2010 at 20:02 | history | edited | mathy | CC BY-SA 2.5 |
edited body; edited title
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| Mar 5, 2010 at 19:40 | history | edited | mathy | CC BY-SA 2.5 |
added 279 characters in body
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| Mar 5, 2010 at 19:21 | answer | added | Jacques Carette | timeline score: 15 | |
| Mar 5, 2010 at 19:16 | history | asked | mathy | CC BY-SA 2.5 |