0
$\begingroup$

Consider the following integral:

$$S(q)=\int_{x=2}^q\sin^2\left(\frac{π\Gamma(x)}{2x}\right)dx$$

And consider functions :

$$R(q)=\frac{q}{\log(q)}$$

$$T(q)=\int_2^q\frac{1}{\log(x)}dx$$

I want to compare them with each other ( at least numerically for large interval of value )

If graph for very large intervals (upto atleast $10^4$) possible please add ( please add all the graph in one axis system so I can compare them ).

(Due to wild oscillations of $S(q)$; I can't deal with it )( Mathematica doesn't seem to help with large values ).

(Does numerics suggests $S(q) \sim R(q)$ or $T(q)$? ).

See ; Related : Towards a new proof of infinitude of primes ( with possible unified application to other primes of special forms whose Infinitude is unknown):

$\endgroup$
  • 1
    $\begingroup$ If I understand correctly, you want a graph of those three function with $2\le q\le10^4$? $\endgroup$ – Jan Eerland May 7 at 13:55
  • $\begingroup$ @Jan yes! That's what I want $\endgroup$ – Bambi May 7 at 13:57
  • $\begingroup$ Why a close vote !? $\endgroup$ – Bambi May 7 at 13:58
  • 1
    $\begingroup$ I already mentioned the link where all the details are mentioned , why to repeat again ? $\endgroup$ – Bambi May 7 at 14:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.