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Timeline for Express MeijerG as integral

Current License: CC BY-SA 4.0

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S Jun 14, 2021 at 14:56 history bounty ended granular_bastard
S Jun 14, 2021 at 14:56 history notice removed granular_bastard
Jun 14, 2021 at 14:56 vote accept granular_bastard
Jun 13, 2021 at 21:10 history edited mikado CC BY-SA 4.0
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Jun 12, 2021 at 13:10 answer added yarchik timeline score: 6
Jun 12, 2021 at 10:53 comment added mikado Of course, the inversion process won't be unique as you can add any function that integrates to zero.
Jun 12, 2021 at 7:31 answer added Roman timeline score: 3
Jun 12, 2021 at 2:07 comment added yarchik Have a look at this link www-m3.ma.tum.de/bornemann/Numerikstreifzug/Chapter9/… It demonstrates how MA comes with MeijerG function for some large class of integrals $\int_0^\infty f_1(x) f_2(\frac{z}{x}) \frac{dx}{x}$ -- the Mellin convolution. Indeed, all you integrals belong to this class. It should be possible to revert the procedure.
Jun 11, 2021 at 15:22 history edited granular_bastard CC BY-SA 4.0
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Jun 11, 2021 at 12:55 history edited granular_bastard CC BY-SA 4.0
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Jun 11, 2021 at 12:41 history edited granular_bastard CC BY-SA 4.0
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Jun 11, 2021 at 11:38 history edited granular_bastard CC BY-SA 4.0
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Jun 11, 2021 at 11:14 history edited granular_bastard CC BY-SA 4.0
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Jun 11, 2021 at 11:13 comment added granular_bastard one could expect that MMA has a larger lookup table than my 3 examples, actually I am looking general identities given the G function, I clarified this in the OP
Jun 11, 2021 at 9:47 comment added user64494 @granularbasterd: You present an analogous table for your integral in your question, isn't so?
Jun 11, 2021 at 9:12 comment added granular_bastard By a lookup table
Jun 11, 2021 at 7:10 comment added user64494 Think of a simpler problem: Integrate[Exp[-k*x],{x,0,Infinity},Assumptions->k>=0] performs 1/k. How to restore that integral from 1/k?
Jun 10, 2021 at 22:45 history edited granular_bastard CC BY-SA 4.0
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Jun 10, 2021 at 21:58 history edited granular_bastard CC BY-SA 4.0
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Jun 10, 2021 at 21:36 history edited granular_bastard CC BY-SA 4.0
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Jun 10, 2021 at 21:26 history edited granular_bastard CC BY-SA 4.0
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Jun 10, 2021 at 20:20 history edited granular_bastard CC BY-SA 4.0
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Jun 10, 2021 at 20:14 history edited granular_bastard CC BY-SA 4.0
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S Jun 10, 2021 at 9:38 history bounty started granular_bastard
S Jun 10, 2021 at 9:38 history notice added granular_bastard Authoritative reference needed
Jun 9, 2021 at 6:00 history tweeted twitter.com/StackMma/status/1402505745481011201
Jun 8, 2021 at 18:59 answer added mikado timeline score: 2
Jun 8, 2021 at 14:32 comment added mikado With a change of variables, your desired integral could represent a Laplace transform. So perhaps change variables x->x s and inverse transform
Jun 8, 2021 at 12:36 history edited granular_bastard CC BY-SA 4.0
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Jun 8, 2021 at 12:32 comment added mikado Perhaps you could use InverseLaplaceTransform?
Jun 8, 2021 at 11:12 history edited granular_bastard CC BY-SA 4.0
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Jun 8, 2021 at 10:08 history edited granular_bastard CC BY-SA 4.0
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Jun 8, 2021 at 8:50 history edited xzczd CC BY-SA 4.0
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Jun 8, 2021 at 8:24 history asked granular_bastard CC BY-SA 4.0