Comparison of integrals with a function (at least numerically):

Asked May 07 '20 at 13:48

Active May 14 '20 at 18:50

Viewed 66 times

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 $T(q)$? ).

edited May 14 '20 at 18:50

asked May 07 '20 at 13:48

bambi

1

If I understand correctly, you want a graph of those three function with $2\le q\le10^4$? – Jan Eerland May 07 '20 at 13:55
@Jan yes! That's what I want – bambi May 07 '20 at 13:57
Why a close vote !? – bambi May 07 '20 at 13:58
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I already mentioned the link where all the details are mentioned , why to repeat again ? – bambi May 07 '20 at 14:06

0 Answers0