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clathratus
  • Member for 3 years, 10 months
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  • San Francisco, CA, USA
33 votes
1 answer
775 views

Freaky dots in the complex plane

24 votes
2 answers
642 views

A magnificent series for $\pi-333/106$

23 votes
3 answers
880 views

product= $\exp\left[\frac{47\mathrm G}{30\pi}+\frac34\right]\left(\frac{11^{11}3^3}{13^{13}}\right)^{1/20}\sqrt{\frac{3}{7^{7/6}\pi}\sqrt{\frac2\pi}}$

21 votes
8 answers
4k views

Request for crazy integrals

21 votes
9 answers
1k views

Relationship between Catalan's constant and $\pi$

19 votes
2 answers
497 views

$\int_{-\infty}^{\infty}\frac{\mathrm{d}x}{ax^2+bx+c}=\pi$ similar identities

19 votes
2 answers
1k views

Integral $T_n=\int_{0}^{\pi/2}x^{n}\ln(1+\tan x)\,dx$

17 votes
2 answers
2k views

What even *are* elliptic functions?

15 votes
3 answers
1k views

Solving the integral $\int_0^{\pi/2}\log\left(\frac{2+\sin2x}{2-\sin2x}\right)\mathrm dx$

15 votes
1 answer
566 views

On the integral $\int_0^1\frac{\arctan\sqrt{t^2+a}}{(t^2+b)\sqrt{t^2+a}}dt$

14 votes
6 answers
2k views

Evaluate $\int_{-\pi/4}^{\pi/4}\frac{x}{\sin x}\mathrm{d}x$

14 votes
3 answers
358 views

A conjecture regarding products of $u(x)=x+\frac1x$

13 votes
3 answers
512 views

Close-form for integral $T(n)=\int_0^{\pi/2}\frac{1}{1+\sin^n(x)}dx$

12 votes
1 answer
269 views

Is there an integral for $\frac{\pi}{\mathrm{G}}$?

12 votes
4 answers
541 views

prove $\int_0^\infty \frac{\log^2(x)}{x^2+1}\mathrm dx=\frac{\pi^3}{8}$ with real methods

11 votes
4 answers
452 views

Closed form for $f(x)=\ _3F_2\left(\tfrac12,\tfrac12,\tfrac12;\tfrac32,\tfrac32;x\right)$

10 votes
2 answers
545 views

Applications of Ramanujan's Master Theorem

10 votes
1 answer
148 views

Solve differential equation: $f'''(x)=f(x)f'(x)f''(x)$

9 votes
1 answer
196 views

Irresistible: $T(p)=\int_0^{\pi/2}x\tan(x)^p\mathrm dx$ for $-2<p<1$

9 votes
2 answers
239 views

Evaluating $S(n)=\int_0^{\pi/2} \log(\sin x)^n\mathrm dx$

8 votes
1 answer
162 views

Evaluating $\int_0^1 \frac{\mathrm dx}{(x^2+ax+1)^{n+1}}$ with real methods

8 votes
1 answer
169 views

Fibonacci sum: $\sum\limits_{k\ge0}\frac{F_{2k+1}}{2k+1}\left(\frac{2+2\sqrt{2}}{1+\sqrt{\frac{17+8\sqrt{2}}{5}}}\right)^{2k+1}(-\frac{1}{5})^k$

8 votes
2 answers
326 views

Solve differential equation $f''''(x)=f'''(x)f''(x)f'(x)f(x)$

8 votes
1 answer
185 views

On $\int_0^\infty \frac{\exp(-x^2)}{1+x^2}dx=\frac{\pi e}2\text{erfc}(1)$

8 votes
3 answers
233 views

Prove that $\sum_{n=0}^{\infty}\frac{\Gamma^2(n+1)}{\Gamma(2n+2)}=\frac{2\pi}{3^{3/2}}$

7 votes
5 answers
193 views

On $\int_0^{2\pi}e^{\cos2x}\cos(\sin2x)\ \mathrm{d}x=2\pi$

7 votes
1 answer
192 views

$\sum\limits_{m\geq1}\sum\limits_{n\geq1}\frac{(-1)^n}{n^3}\sin\left(\frac{n}{m^2}\right)=\frac{\pi^6}{11340}-\frac{\pi^4}{72}$ Numerical evidence

7 votes
6 answers
614 views

How does one solve $\sin x-\sqrt{3}\ \cos x=1$?

7 votes
2 answers
377 views

"Milk" the integral $\int_0^\infty\left(\frac{x^2}{x^4+2ax^2+1}\right)^r\frac{x^2+1}{x^2(x^s+1)}\mathrm dx$

7 votes
1 answer
195 views

closed form for $\int_0^1\frac{\mathrm{Li}_s(x-x^2)}{x-x^2}\mathrm dx$

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