Timeline for Asymptotic difference between a function and its "binomial average"
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Jan 31, 2018 at 17:52 | comment | added | Hans | I suppose your question and answer generalize to when $\frac1{2^n}$ is replaced by $p^kq^{n-k}$ for $p\in(0,1)$? | |
| Jan 31, 2018 at 17:44 | comment | added | Hans | Wow, I just happened upon your question. This is exactly a generalization of my question on both mathoverflow.net/q/291772/32660 and math.stackexchange.com/q/2625685/64809. Would you care to add your opinion on at least the mathoverflow.net site? | |
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Feb 21, 2011 at 6:15 | history | edited | Mike Spivey |
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| Feb 19, 2011 at 0:59 | vote | accept | Mike Spivey | ||
| Feb 17, 2011 at 23:26 | vote | accept | Mike Spivey | ||
| Feb 17, 2011 at 23:30 | |||||
| Feb 17, 2011 at 23:17 | answer | added | Mike Spivey | timeline score: 5 | |
| Nov 22, 2010 at 1:14 | comment | added | Mike Spivey | @Gerry Myerson: Thanks. I am familiar with binomial transforms, but unfortunately nothing that I know about them has helped me thus far with this question. | |
| Nov 21, 2010 at 23:29 | comment | added | Gerry Myerson | There is something called the "binomial transform" of a sequence, which is not exactly what you've got but close enough that maybe some of what's known about it could rub off. | |
| Nov 21, 2010 at 21:19 | comment | added | Mike Spivey | @Gerry Myerson: If we use $\log n = H_n − \gamma +O(\frac{1}{n})$ (and taking $\log 0 = 0$ or just starting the summation at $k=1$) we get that the limit with $f(n)= \log n$ is $\ln 2$ once again. So I guess that proves that if $f$ does have logarithmic growth, then the limit will be finite and nonzero. So now we're just left with the question about functions with other kinds of sublinear growth. | |
| Nov 21, 2010 at 0:28 | comment | added | Gerry Myerson | Can you evaluate the limit in the case $f(n)=\log n$? | |
| Nov 20, 2010 at 23:10 | answer | added | Aaron Meyerowitz | timeline score: 1 | |
| Nov 20, 2010 at 21:46 | history | asked | Mike Spivey | CC BY-SA 2.5 |