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mrtaurho

"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful" - Georg Cantor

Contact: mrtaurho[at]gmail[dot]com

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22 A Series For the Golden Ratio Dec 30 '18
17 Show that $\sum\limits_{n\ge1}\frac1{n^2}=\sum\limits_{n\ge1}\frac3{n^2\binom{2n}n}$ without actually evaluating both series Dec 24 '18
16 What is the dot in “$1.2.4$”? Mar 13 '19
15 How to find $\int_0^{{\pi}/{2}} (\pi x-4x^2)\log(1+\tan x)\mathrm dx$ May 10 '19
15 A particular vanishing integral Aug 12 '19
13 On the integral $I(a)=\int_0^1\frac{\log(a+t^2)}{1+t^2}\mathrm dt$ Nov 11 '18
13 Evaluate$\int\limits_0^1 [\log(x)\log(1-x)+\operatorname{Li}_2(x)]\left[\frac{\operatorname{Li}_2(x)}{x(1-x)}-\frac{\zeta(2)}{1-x}\right]\mathrm dx$ Dec 14 '18
13 Is $\int\limits_0^\infty\frac{\sin y}{y^{s+1}}dy=-\Gamma(-s)\sin(\frac{\pi s}{2})$ for $\operatorname{Re}(s)\in (-1,0)$ obvious? Dec 30 '18
12 Can you compute $\int_0^1\frac{\log(x)\log(1-x)}{x}dx$ more precisely than $1.20206$ and do a comparision with $\zeta(3)$? Apr 26 '19
12 Prove that $\int_0^1\frac{\operatorname{Li}_3(1-z)}{\sqrt{z(1-z)}}\mathrm dz=-\frac{\pi^3}{3}\log 2+\frac{4\pi}3\log^3 2+2\pi\zeta(3)$ Oct 5 '18
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