# Plot of ratio of two integrals:

Consider the following integrals $$I_1(x) =\int_0^\infty\mathrm dy \frac{F(x + \mathrm iy) − F(x −\mathrm iy)}{\mathrm e^{2πy}-1},$$

And

$$I_2(x) =\int_1^x F(t)dt$$

Where, $$F(z) = \sin^2[π\Gamma(z)/(2z)]$$

I want to plot (with considerable accuracy) $$R(x)=I_1(x)/I_2(x)$$

Also , see if it's apparent from plot : $$R(x)\rightarrow0$$ as $$x\rightarrow\infty$$

I want growth rate of local minimas and Maximas of $$I_1(x)$$ as $$x\rightarrow\infty$$

See this MSE post for more details .

• This is in essence a duplicate of a previous question asked on this forum. The problems discussed there are all the same here. – Wolfgang Bangerth May 18 '20 at 22:31
• @WolfgangBangerth I asked for second Integral in previous question , first Integral is new here and equally tricky . – bambi May 19 '20 at 8:03
• @Bambi as far as I can tell it's "tricky"' in the same way the other integrals were. – Spencer Bryngelson May 22 '20 at 15:02