Timeline for $\int_L^\infty \exp(- t - y/t) \, dt = \text{?}$
Current License: CC BY-SA 4.0
14 events
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| Jun 10, 2023 at 22:21 | comment | added | H A Helfgott | I think your second answer is particularly nice. Let me adapt to $r\geq 1$ (which is the simpler case) and possibly simplify it a little - I'll post an answer below. | |
| Jun 8, 2023 at 19:25 | comment | added | Iosif Pinelis | @HAHelfgott : Do you have a further response to this and other answers? | |
| Jun 6, 2023 at 12:23 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 6, 2023 at 10:45 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 6, 2023 at 1:49 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 6, 2023 at 1:16 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 6, 2023 at 1:12 | comment | added | Iosif Pinelis | @HAHelfgott : You were right, the case $r\in(0,1)$ is different, because here $t$ may take values close to the point $2$ of singularity of $F$. Now this case is done as well, anyhow. | |
| Jun 6, 2023 at 1:10 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 5, 2023 at 22:13 | comment | added | H A Helfgott | Right, I'm wondering why small and large $r$ are equally from your perspective, since they aren't from mine. | |
| Jun 5, 2023 at 22:02 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 5, 2023 at 22:02 | comment | added | Iosif Pinelis | @HAHelfgott : I think the twice repeated integration by parts as in this answer will work for $r\in(0,1)$ as well -- because $F'<0$ and $F''>0$ on the entire interval $(2,\infty)$. I just don't have time to do this in detail at this point. (Also, I think your upper bound for $L>\sqrt y$ is essentially the same as my upper for $r>1$.) | |
| Jun 5, 2023 at 21:57 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jun 5, 2023 at 21:49 | comment | added | H A Helfgott | I'm especially interested in the case $r\in (0,1)$ - one can give a very simple upper bound in the case $r>1$, as in my brief self-answer. | |
| Jun 5, 2023 at 21:43 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |