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6h
answered Prove $\sup_x|u_x(x,t)|\le Ct^{-\frac{3}{4}}\|f\|_2$ for all $t>0$.
7h
answered Closed-form of $\int_0^1 x^n \operatorname{li}(x^m)\,dx$
8h
answered Rational solutions to $a+b+c=abc=6$
11h
answered Proving an Inequality using a Different Method
11h
answered $p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
11h
comment Finding a point using complex geometry
Our $C$ points are a little different, who's right?
11h
answered Finding a point using complex geometry
13h
awarded  Nice Answer
14h
awarded  geometry
14h
answered Conjecture about integral $\int_0^1 K\left(\sqrt{\vphantom1x}\right)\,K\left(\sqrt{1-x}\right)\,x^ndx$
14h
comment Conjecture about integral $\int_0^1 K\left(\sqrt{\vphantom1x}\right)\,K\left(\sqrt{1-x}\right)\,x^ndx$
Zhou deals with similar integrals in arxiv.org/pdf/1301.1735. An effective technique is to exploit $$ K(k) = 2\sum_{n\geq 0}\frac{P_n(2k-1)}{2n+1}$$ like I did here. Shifted Legendre polynomials give an orthogonal base of $L^2(0,1)$, so $\mathcal{J}(n)$ is easily related with the series $$\sum_{n\geq 0}\frac{(-1)^n}{(2n+1)^3}=\frac{\pi^3}{32}.$$
14h
comment Conditions on $f$ to have $ \int_{x=0}^1\int_{y=0}^1\int_{z=0}^1 \frac{f(x)}{(x-y)^2 (y-z)} dz dy dx $ finite?
The problem is not in the regularity of $f$, the problem is that $$\int_{0}^{1}\frac{dz}{y-z}$$ is not well-defined for any $y\in(0,1)$. Do you want to compute the principal value of the integral?
15h
revised Closed-forms of the integrals $\int_0^1 K(\sqrt{k})^2 \, dk$, $\int_0^1 E(\sqrt{k})^2 \, dk$ and $\int_0^1 K(\sqrt{k}) E(\sqrt{k}) \, dk$
added 113 characters in body
15h
revised Closed-forms of the integrals $\int_0^1 K(\sqrt{k})^2 \, dk$, $\int_0^1 E(\sqrt{k})^2 \, dk$ and $\int_0^1 K(\sqrt{k}) E(\sqrt{k}) \, dk$
added 687 characters in body
16h
comment Simplifying Series of Gamma Function
@KendrickFong: by the well-known rule for which the sum of the inverses is the inverse of the sum ?! :P
16h
comment Improper integral parametrised in complex variable: when is it holomorphic?
@harlekin: exactly.
16h
comment Simplifying Series of Gamma Function
If $b$ is a negative integer one of the term of the series depends on $\Gamma$ evaluated in one of its poles.
16h
answered Simplifying Series of Gamma Function
16h
answered Improper integral parametrised in complex variable: when is it holomorphic?
16h
answered Closed-forms of the integrals $\int_0^1 K(\sqrt{k})^2 \, dk$, $\int_0^1 E(\sqrt{k})^2 \, dk$ and $\int_0^1 K(\sqrt{k}) E(\sqrt{k}) \, dk$