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Mathematics
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Nomas2
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10
How did Ramanujan find $\sum_{n=0}^\infty (-1)^n\frac{(1/2)_n(1/4)_n(3/4)_n}{n!^3}\frac{644n+41}{25920^n}=\frac{288\sqrt{5}}{5\pi}?$
Apr 13
9
Given algebraic $a$, find the closed form of $\int_0^a \dfrac{dx}{\sqrt{1-x^4}}$
Sep 30, 2023
6
Euler's proof of $\frac{\pi}{6}=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-\cdots$
Dec 1, 2023
5
Minimal polynomial of $\operatorname{cd}\frac{4K}{n}$
Oct 2, 2023
5
On $\int_0^1\prod_{k=1}^\infty (1-x^k)\, dx$
Oct 28, 2023
5
Is $\cos$ a polynomial function of $\sin$?
Nov 22, 2023
4
Applying Whittaker's and Watson's Lagrange theorem to $\sin$
Mar 27
3
Proving $\sum_{n=-\infty}^\infty n^2e^{-\pi n^2}=\frac{\Gamma (1/4)}{4\sqrt{2}\pi^{7/4}}$
Oct 24, 2023
3
Proof that $\zeta (z)=\frac{\sigma '(z)}{\sigma (z)}$
Oct 25, 2023
3
Can we formally multiply out infinite products?
Nov 13, 2023
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Euler's proof of $\frac{\pi}{6}=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-\cdots$
5
Is $\int \operatorname{sn}^2u\,\mathrm du$ really irreducible?