Timeline for Asymptotics of the sum $\sum_{n=1}^\infty \frac{x^n}{n^n}$
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jan 12, 2019 at 13:37 | audit | Low quality posts | |||
| Jan 12, 2019 at 13:37 | |||||
| Dec 26, 2018 at 19:56 | vote | accept | Franklin Pezzuti Dyer | ||
| Dec 26, 2018 at 19:49 | comment | added | Clement C. | Updated to give slightly tighter lower bound, and better upper bound, and explain a general method to improve them incrementally. | |
| Dec 26, 2018 at 19:48 | history | edited | Clement C. | CC BY-SA 4.0 |
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| Dec 26, 2018 at 0:55 | comment | added | Clement C. | Should be fixed (except for something inconsequential in the plot, which changes nothing). Now, back to my second flight. | |
| Dec 26, 2018 at 0:54 | history | edited | Clement C. | CC BY-SA 4.0 |
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| Dec 25, 2018 at 19:56 | comment | added | Mason | +1. Good answer. I am going to see if we can use Abel's summation formula to corroborate this work. If I find a way of doing that I will try and write it up. | |
| Dec 25, 2018 at 19:54 | comment | added | Will Jagy | OR take $g(x) = \frac{f(x)}{e^{x/e}},$ where you have proved that $g' > 0$ | |
| Dec 25, 2018 at 19:50 | comment | added | Mason | "Please make sure your table is in the upright position. We'll be taking off shortly... "No!!! But Frpzzd will enjoy this explanation so much more if there is a graph!!!" "Sir... please put the laptop away. " | |
| Dec 25, 2018 at 19:35 | comment | added | Clement C. | Note 2: actually, f(0)=0. This won't change much and the conclusion stands, but the answer needs to be edited. I'll do it when landing. | |
| Dec 25, 2018 at 19:24 | comment | added | Clement C. | Note: I believe the lower bound to be tight, i.e., $\log f(x) = x/e +o(x)$. One can get closer to the constant $1/e$ by the above approach, by treating the first few terms of the series separately to get a better differential equation lower bound (since higher terms allow a better bound on $(1+1/n)^n$). | |
| Dec 25, 2018 at 19:09 | history | edited | Clement C. | CC BY-SA 4.0 |
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| Dec 25, 2018 at 19:04 | history | edited | Clement C. | CC BY-SA 4.0 |
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| Dec 25, 2018 at 18:47 | history | answered | Clement C. | CC BY-SA 4.0 |