Timeline for Express MeijerG as integral
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 14, 2021 at 14:56 | history | bounty awarded | granular_bastard | ||
| Jun 14, 2021 at 14:56 | vote | accept | granular_bastard | ||
| Jun 13, 2021 at 12:49 | comment | added | yarchik | @granularbastard In the function MeijerGIntegral the result of Mellin transform s typically contains a product of several Gamma functions. Next, I split it into a product of two terms sA and sB, where sA necessarily contains Gamma. This splitting is not unique. If you would like to have a different result, you need to split in a different way making sure that for both sA and sB the InverseMellinTransform exists. | |
| Jun 13, 2021 at 12:41 | comment | added | granular_bastard | The given routine works for the examples of the OP, but for other examples it returns a result that contains another shorter Meijer G-function. How to deal in these cases? Example: MeijerGIntegral[ MeijerG[{{}, {}}, {{0, 1/2, 1, 3/2, 2, 5/2, 3}, {}}, x], x, t] Result: Exp[-Sqrt[t]] Sqrt[Pi]/t MeijerG[{{},{}},{{1,3/2,2,5/2,3},{}},4x/t] | |
| Jun 12, 2021 at 17:56 | history | edited | yarchik | CC BY-SA 4.0 | explanation is added. |
| Jun 12, 2021 at 17:46 | comment | added | yarchik | @mikado Thank you! In fact I am choosing among a smaller number of possibilities for the given examples. The Mellin transform will typically be given by a product of several Gamma functions. I choose on of them for the inverse Mellin and hope that the inverse Mellin can be done for the rest. There is no guarantee. In principle, one should try all possibilities and select the simplest answer. I will add a couple of sentences into my post. | |
| Jun 12, 2021 at 14:48 | comment | added | mikado | This is really good. It would be nice to have some explanation of how it works. I think you are choosing arbitrarily 1 of 6? possible answers. It would be interesting to see all of them (we could perhaps choose the simplest). | |
| Jun 12, 2021 at 13:10 | history | answered | yarchik | CC BY-SA 4.0 |