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My name is John (he/him/his). I'm a math major at UC San Diego. I love integrals and infinite series. Here's a list of my favorite posts.
Questions:
- Freaky dots in the complex plane
- A Crazy Infinite Product
- One of the worst integrals ever
- A magnificent series for $\pi-333/106$
Answers:
- How to integrate $\int_{0}^{2\pi} \frac{1}{\sin^4x + \cos^4 x} dx$
- Show that $\int_{0}^{\pi/4}\int_{0}^{\pi/4}\left(\sec(x+y)+\sec(x-y)\right)\mathrm{d}x\mathrm{d}y=2G$
- List of integrals or series for Gieseking's constant $\rm{Cl}_2\big(\tfrac{\pi}3\big)$?
- Generalizing $\sum\limits_{m\geq1}\sum\limits_{n\geq1}\frac{(-1)^n}{n^3}\sin(n/m^{2k})=\frac1{12}\zeta(6k)-\frac{\pi^2}{12}\zeta(2k)$
- Evaluating $\int_{0}^{2 \pi} \frac{\sin(\phi)}{(\sin(\theta)-\sin(\phi))^2+2a(1-\cos(\theta -\phi))} d\phi$
- Unexpected appearances of $\pi^2 /~6$.
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