Timeline for Inverse Stieltjes Transform Implementation?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Oct 23 at 13:53 | history | bounty ended | Yaroslav Bulatov | ||
| Oct 17 at 1:55 | comment | added | Vitaliy Kaurov | Could you please add / crosspost your answer on Community, that would be highly appreciated: community.wolfram.com/groups/-/m/t/3295143 | |
| Oct 13 at 9:49 | comment | added | Mariusz Iwaniuk | @YaroslavBulatov I updated my answer for more one definition of Inverse Stieltjes Transform. | |
| Oct 13 at 9:46 | history | edited | Mariusz Iwaniuk | CC BY-SA 4.0 |
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| Oct 13 at 0:49 | comment | added | Yaroslav Bulatov | I have a draft ready, will add a section linking to more of these inverse laplace techniques before posting | |
| Oct 12 at 22:21 | comment | added | Yaroslav Bulatov |
Thanks, this is useful reference! (will link in an overview of techniques on wolfram community soon). PS, I found this simple case of Stieltjes transform works out of the box (a little confused by - sign in the result, whether it's a bug) S[z_] = (2 ArcCoth[Sqrt[z]])/Sqrt[z]; expr = 1/Pi Limit[ Im@ComplexExpand@S[x + I \[CurlyEpsilon]], \[CurlyEpsilon] -> 0]; Assuming[{0 < x < 1}, expr // FullSimplify]
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| Oct 12 at 22:19 | history | edited | Mariusz Iwaniuk | CC BY-SA 4.0 |
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| Oct 12 at 22:09 | comment | added | Mariusz Iwaniuk | @YaroslavBulatov I updated my answer. | |
| Oct 12 at 22:07 | history | edited | Mariusz Iwaniuk | CC BY-SA 4.0 |
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| Oct 12 at 21:13 | history | edited | Mariusz Iwaniuk | CC BY-SA 4.0 |
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| Oct 12 at 13:57 | vote | accept | Yaroslav Bulatov | ||
| Oct 11 at 7:57 | history | edited | Mariusz Iwaniuk | CC BY-SA 4.0 |
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| Oct 11 at 6:00 | comment | added | Yaroslav Bulatov |
I expected formula from wikipedia to work, but it produces 0 S[x_] := ArcTanh[1/Sqrt[x]]/Sqrt[x]; Limit[(S[x - I eps] - S[x + I eps])/(2 I Pi), eps -> 0, Direction -> "FromAbove"]
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| Oct 11 at 5:47 | comment | added | Yaroslav Bulatov |
Added ilaplaceMellinTrig function that uses this trick here, right now ilaplaceMellinTrig, ilaplaceMellin and ilaplaceFeynmann utils in that file seem to cover most of my use-cases (thanks mostly to your help)
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| Oct 10 at 9:54 | history | answered | Mariusz Iwaniuk | CC BY-SA 4.0 |