Timeline for Closed-form Solution for series involving incomplete Gamma Function
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 2, 2016 at 13:11 | vote | accept | Aaron Hendrickson | ||
| Jul 25, 2016 at 15:28 | vote | accept | Aaron Hendrickson | ||
| Aug 2, 2016 at 13:11 | |||||
| Jul 25, 2016 at 15:28 | vote | accept | Aaron Hendrickson | ||
| Jul 25, 2016 at 15:28 | |||||
| Jul 25, 2016 at 12:28 | history | edited | Harry Peter | edited tags | |
| Jul 22, 2016 at 15:52 | answer | added | Harry Peter | timeline score: 3 | |
| Jul 13, 2016 at 23:00 | vote | accept | Aaron Hendrickson | ||
| Jul 25, 2016 at 15:28 | |||||
| Jul 11, 2016 at 19:42 | comment | added | Aaron Hendrickson | Thanks Jack. I will take a look at it. It may be that there is no closed form solution. If no better answer arises I will accept what you posted. | |
| Jul 11, 2016 at 17:14 | comment | added | Jack D'Aurizio | I carried on some computations for the general case, and I am left with a hypergeometric function as a main term and a series of $\phantom{}_{2} F_2$ functions as secondary term, that does not seem to simplify further. I hope that helps. | |
| Jul 11, 2016 at 17:09 | answer | added | Jack D'Aurizio | timeline score: 1 | |
| Jul 11, 2016 at 14:24 | history | edited | Aaron Hendrickson | CC BY-SA 3.0 | added 356 characters in body |
| Jul 11, 2016 at 14:17 | comment | added | Aaron Hendrickson | Jack, I have solved this problem for the case where $\alpha$ and $\beta$ are integers using ibp where $u={_{1}}F_{1}(-\alpha;-\beta,-\lambda x)$ and $\mathrm{d}v = e^{ax}$. I could include that answer in the post but the answer is still a series as a result of using ibp. And i'm not sure how it will help me get to the general solution. | |
| Jul 11, 2016 at 14:11 | comment | added | Jack D'Aurizio | If $\alpha,\beta\in\mathbb{N}$, your hypergeometric function is just a polynomial and the closed form is straightforward to compute. It shouldn't be terribly difficult to generalize such closed form for non-integer values of $\alpha,\beta$. | |
| Jul 11, 2016 at 14:07 | history | asked | Aaron Hendrickson | CC BY-SA 3.0 |