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Martin.s
  • Member for 1 year, 3 months
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Hey everyone! I’m an 18-year-old math enthusiast and chess lover (rated 2100 on Chess.com). I’m passionate about a wide range of topics, including number theory, automorphic forms, representation theory, quantum field theory, positive definite lattices, hyperbolic reflection groups, algebraic geometry, arithmetic combinatorics, analytic number theory, compressed sensing, and algebraic combinatorics.In my free time, I solve integrals or create new ones in my head and post them online.

You might know me, but you don’t really know me.

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Conjectured closed form of $\int_0^1 \frac{\text{Li}_2\left(\frac{x}{4}\right)}{4-x}\,\log\left(\frac{1+\sqrt{1-x}}{1-\sqrt{1-x}}\right)\,dx$
Feb 24
question
5
Conjectured closed form of $\int\limits_0^1 \frac{\ln y \operatorname{Li}_2 (-y)}{1-y^2} \, dy$
Mar 4
question
1
Conjectured closed form of $\int_0^1\frac{\ln^3(1+x)\,\ln^3x}x\mathrm{d}x$
Mar 7
answer
1
Conjectured closed form of $\int\limits_0^1 \frac{\ln y \operatorname{Li}_2 (-y)}{1-y^2} \, dy$
May 30
answer
0
Structural differences between closed forms of two related infinite products?
Feb 25
answer
0
Is there any sequence $a_n$ of nonnegative numbers for which $\sum_{n \geq 1}a_n^2 <\infty$ and $\sum_{n \geq 1}\left(\sum_{k \geq 1}\frac{a_{kn}}{k}\right)^2=\infty$?
Sep 20
answer
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Number of collinear ways to fill a grid
Sep 20
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15
Show that $\int_{-\pi/2}^{\pi/2}\sin(\tan(\tan(x)))\tan(x)dx=\frac{\pi}{e^{(e^2-1)/(e^2+1)}}-\frac{\pi}{e}$
14
How to evaluate $\int_{0}^{\frac{\pi}{2}} \frac{\cos(x)}{(1 + \sqrt{\sin(2x)})^n} \,dx$
13
Prove that if $\{a_{k}\}$ is a sequence of real numbers such that $\sum_{k=1}^{\infty} \frac{|a_{k}|}{k} = \infty$,
12
Does a Fixed Sequence of Moves Solve Any Rubik's Cube Configuration When Repeated Enough Times?
11
Show that $\sum_{n=1}^{+\infty}\frac{1}{(n\cdot\sinh(n\pi))^2} = \frac{2}{3}\sum_{n=1}^{+\infty}\frac{(-1)^{n-1}}{(2n-1)^2} - \frac{11\pi^2}{180}$