Timeline for T functions arising from derivatives of incomplete Gamma function
Current License: CC BY-SA 4.0
21 events
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| Nov 7, 2023 at 21:19 | comment | added | Iosif Pinelis | @user18722294 : I have added further details on this. | |
| Nov 7, 2023 at 21:18 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 7, 2023 at 20:52 | comment | added | user18722294 | Pinels alright, can you specify in which order you consider the limit $x \to \infty$, before or inside the integral? If latter, why is it justified? | |
| Nov 6, 2023 at 15:38 | comment | added | Iosif Pinelis | @user18722294 : I did not use the l'Hospital rule to obtain the asymptotic behavior of the $k$th derivative of $\ln^p$ -- the latter can be obtained by induction on $k$. I used the l'Hospital rule and the asymptotic behavior of the $k$th derivative of $\ln^p$ to obtain the second equality in (2). | |
| Nov 6, 2023 at 10:57 | comment | added | user18722294 | could you elaborate on how you used l'Hôpital to obtain the asymptotic behaviour of the k-the derivative of $\ln^p$? @Isofi Pinelis | |
| Oct 28, 2023 at 7:14 | comment | added | user18722294 | I accepted it, thanks a lot! | |
| Oct 28, 2023 at 7:13 | vote | accept | user18722294 | ||
| Oct 25, 2023 at 16:16 | comment | added | Iosif Pinelis | @user18722294 : I never used or mentioned a full asymptotic expansion. As stated in the answer, I just used the partial expansion (2), with $k=3$ and $g\in\{g_1,g_2\}$. Details of the straightforward calculations are presented in the pdf image of a Mathematica notebook at u.pcloud.link/publink/… . Please let me know if anything here still seems unclear.. | |
| Oct 25, 2023 at 15:03 | comment | added | user18722294 | Thanks @Iosif! I followed your derivation, yet I wonder how it works out that you truncate the integral up to $\mathcal{o}(1)$ while the full asymptotic expansion of the integral diverges (see math.stackexchange.com/questions/4789344/…). | |
| Oct 25, 2023 at 3:22 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 24, 2023 at 21:10 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 24, 2023 at 20:53 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 24, 2023 at 20:44 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 24, 2023 at 20:39 | comment | added | Iosif Pinelis | I have now added the details. | |
| Oct 24, 2023 at 20:39 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 24, 2023 at 20:33 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 24, 2023 at 16:34 | comment | added | user18722294 | I would be very happy about the details, because my initial goal is to understand $g_2(x)$ and I've hoped that this could be achieved via $T(4,1,x)$. | |
| Oct 24, 2023 at 13:55 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 24, 2023 at 13:29 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 24, 2023 at 13:18 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 24, 2023 at 13:09 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |