# High accuracy computation question on MO

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 ?

• 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. – Martin Sleziak May 14 at 18:52
• 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. – András Bátkai May 16 at 8:47
• 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. – LSpice May 16 at 19:26
• @LSpice I'm reevaluating myself wrt standards of MO . – Bambi May 16 at 19:32
• 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. – Ryan Budney May 17 at 2:34
• 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. – David Roberts May 17 at 6:44
• 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. – Timothy Chow May 28 at 23:26