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Can I ask question which require very high accuracy calculation with very delicate nature on MO :

Ex: calculate: $$S(q)=\int_{x=2}^q\sin^2\left(\frac{π\Gamma(x)}{2x}\right)dx$$ for $q=10^3$ or $10^4$

Mathematica doesn't seem to help me with this.

This will require very high efficiency calculation

Is there any other forum where I can put this type of question ?

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    $\begingroup$ There is Computational Science on Stack Exchange network. However, I am not very familiar with that site, so I am not the right person to judge what kind of question is on-topic/off-topic there. $\endgroup$
    – Martin Sleziak
    May 14, 2020 at 18:52
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    $\begingroup$ I am sure you can ask this here if you ask for advice/methods. If you look for a software, then this may not be the right place. $\endgroup$
    – András Bátkai
    May 16, 2020 at 8:47
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    $\begingroup$ I know there've been some issues with some past MO questions not being received well, so I really appreciate your taking the time to gauge the mood of the community about what questions are welcome and would do well. $\endgroup$
    – LSpice
    May 16, 2020 at 19:26
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    $\begingroup$ @LSpice I'm reevaluating myself wrt standards of MO . $\endgroup$
    – bambi
    May 16, 2020 at 19:32
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    $\begingroup$ One thing you should have in your question (regardless whether or not you post to MO) is what does "high accuracy" mean. Do you want the answer to one significant digit? 10? 10^10? etc. $\endgroup$
    – Ryan Budney
    May 17, 2020 at 2:34
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    $\begingroup$ This type of numerical analysis question can be rather interesting, when phrased in a general way, say about fast-converging series that calculate the integrand over a wide range of values. $\endgroup$
    – David Roberts Mod
    May 17, 2020 at 6:44
  • $\begingroup$ I agree with David Roberts. The SIAM 100-digit challenge problems amply demonstrate that high-precision numerical calculations can be extremely interesting from a mathematical point of view. $\endgroup$
    – Timothy Chow
    May 28, 2020 at 23:26

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This question (as well as similar questions targeting computations and numerics) is most definitely welcome at Computational Science, where it was eventually posted.

While some Computational Science folks are active on MathOverflow, not all are. So, it might be useful to post it on Computational Science or Computational Science and MathOverflow (not simultaneously, unless rephrased to focus on searching the input targeting a particular community): respecting the cross-posting policy.

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    $\begingroup$ I don't think this really is a computational question. Unless I screwed something up you can get the asymptotics by purely analytical methods -- I wrote up the answer at the other foruma scicomp.stackexchange.com/a/35209/36112 $\endgroup$
    – Lior Silberman
    May 23, 2020 at 5:47
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    $\begingroup$ @LiorSilberman thanks a lot for that answer! it was actually a very interesting approach – I was not able to find any problems with it. While it might not be computational, analytical methods are a part of computational science. IMHO, this type of questions belongs to both communities and allows experts from both fields to add their insight. $\endgroup$
    – Anton Menshov
    May 23, 2020 at 18:13

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