Timeline for Binomial coefficient identity
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 20, 2021 at 6:03 | answer | added | qifeng618 | timeline score: 1 | |
| Nov 20, 2017 at 10:06 | comment | added | darij grinberg | This has also recently appeared on math.stackexchange: math.stackexchange.com/questions/2455428/… | |
| Dec 24, 2016 at 16:19 | comment | added | T. Amdeberhan | @hkju: I've posted a solution. I'm curious, what is the polytope you mentioned? | |
| Dec 24, 2016 at 16:16 | answer | added | T. Amdeberhan | timeline score: 3 | |
| Dec 24, 2016 at 0:40 | answer | added | KConrad | timeline score: 1 | |
| Jan 11, 2015 at 6:11 | comment | added | Ira Gessel | This identity is also a special case of Vandermonde's theorem. | |
| Jan 11, 2015 at 4:43 | answer | added | KConrad | timeline score: 11 | |
| Jan 11, 2015 at 4:06 | answer | added | Todd Trimble | timeline score: 9 | |
| Jan 11, 2015 at 1:53 | answer | added | KConrad | timeline score: 5 | |
| Jan 11, 2015 at 1:51 | answer | added | Gjergji Zaimi | timeline score: 9 | |
| Jan 11, 2015 at 0:10 | answer | added | GH from MO | timeline score: 10 | |
| Jan 10, 2015 at 22:19 | comment | added | hkju | This identity implies that $$ \sum_{k=0}^m \frac {n(-1)^k}{n+k} = \sum_{k=0}^n \frac {m(-1)^k}{m+k}$$. | |
| Jan 10, 2015 at 22:01 | history | edited | hkju | CC BY-SA 3.0 |
added 11 characters in body
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| Jan 10, 2015 at 21:58 | comment | added | hkju | You mean, to reduce $\int_0^1 (1-x)^m x^{n-1} dx $ to $ \frac{m}{n} \int_0^1 (1-x)^{m-1} x^{n} dx $ using integration by parts, and so on..., right ? | |
| Jan 10, 2015 at 16:52 | answer | added | user64494 | timeline score: -2 | |
| Jan 10, 2015 at 16:03 | comment | added | darij grinberg | Somewhat more elementary than the beta integral, whatever it is: use partial integration to reduce computing $\int_0^1 \left(1-x\right)^m x^{n-1} dx$ to computing $\int_0^1 \left(1-x\right)^{m+1} x^n dx$, and proceed by induction over $n$. This is purely algebraic. | |
| Jan 10, 2015 at 15:32 | review | Close votes | |||
| Jan 11, 2015 at 18:56 | |||||
| Jan 10, 2015 at 15:14 | comment | added | Lucia | Look at $\int_0^1 (1-x)^m x^{n-1} dx$ and use the binomial theorem together with the beta integral. | |
| Jan 10, 2015 at 15:11 | history | asked | hkju | CC BY-SA 3.0 |