user avatar
user avatar
user avatar
clathratus
  • Member for 4 years
  • Last seen this week
  • San Francisco, CA, USA
33 votes
1 answer
782 views

Freaky dots in the complex plane

24 votes
2 answers
645 views

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

23 votes
3 answers
887 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
503 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
4 answers
1k views

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

15 votes
1 answer
589 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
361 views

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

13 votes
3 answers
517 views

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

12 votes
1 answer
271 views

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

12 votes
4 answers
551 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
458 views

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

10 votes
2 answers
557 views

Applications of Ramanujan's Master Theorem

10 votes
1 answer
149 views

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

9 votes
1 answer
197 views

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

9 votes
2 answers
241 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
170 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
329 views

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

8 votes
1 answer
187 views

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

8 votes
3 answers
238 views

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

8 votes
2 answers
143 views

Analogs of $\sum_{n\ge1}\frac{n^{13}}{e^{2\pi n}-1}=\frac{1}{24}$

7 votes
1 answer
145 views

Ramanujan: If $\psi(p,n)=\int_0^a\phi(p,x)\cos(nx)dx$, then $\frac\pi2\int_0^a\phi(p,x)\phi(q,nx)dx=\int_0^\infty\psi(q,x)\psi(p,nx)dx$.

7 votes
1 answer
194 views

Is there a closed form for $\int_0^1\,_3F_2(\tfrac14,\tfrac12,\tfrac34;\tfrac23,\tfrac43;x)dx$?

7 votes
5 answers
202 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

1
2 3 4 5 6