Timeline for Closed form for $\int_0^T e^{-x}\frac{I_n(\alpha x)}{x}dx$
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 13, 2017 at 10:20 | history | edited | Alexandre | CC BY-SA 3.0 |
Answer to one of the questions
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| Jun 12, 2017 at 12:19 | history | edited | Alexandre | CC BY-SA 3.0 |
Corrections and more details
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| Jun 12, 2017 at 12:14 | history | edited | Alexandre | CC BY-SA 3.0 |
Corrections and more details
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| Jun 12, 2017 at 8:20 | history | edited | Alexandre | CC BY-SA 3.0 |
deleted 1 character in body
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| Jun 11, 2017 at 16:44 | answer | added | Carlo Beenakker | timeline score: 4 | |
| Jun 11, 2017 at 15:53 | comment | added | Alexandre | Great! I found the incomplete gamma for small $\alpha$ from the first infinite series proposed, and I can also get $\alpha=1$ from the second infinite series but it is expressed with the hypergeometric function ${}_2F_2$. Do you have more detail about this closed expression in terms of $I_0$ and $I_1$? | |
| Jun 11, 2017 at 14:56 | comment | added | Carlo Beenakker | and for small $\alpha$ it's an incomplete gamma function, are these asymptotics of interest? | |
| Jun 11, 2017 at 14:29 | comment | added | Carlo Beenakker | for $\alpha=1$ there is a closed form expression in terms of $I_0(t)$ and $I_1(t)$ | |
| Jun 11, 2017 at 13:32 | comment | added | Alexandre | You are right, it may have no closed form. I asked because this last integral seems to be an unexploited approach. Maybe I should look at the asymptotic behaviour and be satisfied with it. | |
| Jun 11, 2017 at 13:23 | comment | added | Igor Rivin | I don't understand the downvotes. On the other hand, I don't understand why the OP expects a closed form, either... | |
| S Jun 11, 2017 at 11:02 | history | suggested | Glorfindel | CC BY-SA 3.0 |
grammar corrections, thanks removed as per https://meta.stackexchange.com/q/2950/295232
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| Jun 11, 2017 at 11:00 | review | Suggested edits | |||
| S Jun 11, 2017 at 11:02 | |||||
| Jun 11, 2017 at 10:57 | review | First posts | |||
| Jun 11, 2017 at 11:11 | |||||
| Jun 11, 2017 at 10:54 | history | asked | Alexandre | CC BY-SA 3.0 |