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Anon
  • Member for 6 years, 6 months
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52 votes
2 answers
5k views

Why can't Antoine's necklace fall apart?

25 votes
3 answers
849 views

Interesting closed form for $\int_0^{\frac{\pi}{2}}\frac{1}{\left(\frac{1}{3}+\sin^2{\theta}\right)^{\frac{1}{3}}}\;d\theta$

20 votes
4 answers
2k views

Rational function approximation to square root

14 votes
1 answer
352 views

How do we know we get the right answer?

12 votes
2 answers
356 views

Closed form for $\int_0^1...\int_0^1\frac{1}{\left(1+\sqrt{1+x_1^2+...+x_n^2}\right)^{n+1}}\;dx_1...dx_n$

12 votes
2 answers
236 views

Prove known closed form for $\int_0^\infty e^{-x}I_0\left(\frac{x}{3}\right)^3\;dx$

11 votes
0 answers
714 views

More elegant $\zeta(s)$ zeros counting function than $N(T)$

9 votes
1 answer
299 views

How are Trott constants found; are there mathematical results?

8 votes
1 answer
234 views

Prove the recurrence $x_{n}=\frac{x_{n-2}}{1+x_{n-1}}$ converges for a unique $x_1$

8 votes
1 answer
316 views

Accurate identities related to $\sum\limits_{n=0}^{\infty}\frac{(2n)!}{(n!)^3}x^n$ and $\sum\limits_{n=0}^{\infty}\frac{(2n)!}{(n!)^4}x^n$

7 votes
1 answer
293 views

Very accurate approximations for $\sum\limits_{n=0}^\infty \frac{n}{a^n-1}$ and $\sum\limits_{n=0}^\infty \frac{n^{2m+1}}{e^n-1}$

7 votes
0 answers
344 views

Why does this fractal approximate so many others?

7 votes
1 answer
341 views

Simple closed form for $\int_0^\infty\frac{1}{\sqrt{x^2+x}\sqrt[4]{8x^2+8x+1}}\;dx$

7 votes
0 answers
179 views

Origami-constructible numbers

7 votes
0 answers
110 views

Explain approximate lines in graph of this function

6 votes
0 answers
148 views

Closed form for $\sum\limits_{n=1}^\infty\frac{W(n^2)}{n^2}$

6 votes
0 answers
154 views

Accurate $\zeta(s)$ integral identities for $\sum_\limits{n=2}^{\infty}\frac{1}{n^{s}\sqrt{\ln{n}}}$

5 votes
0 answers
159 views

Proportion of cube closer to centre than outside

5 votes
0 answers
262 views

Probability that partition problem has a solution for sets of random integers

5 votes
1 answer
598 views

Series related to the Mandelbrot set

5 votes
2 answers
358 views

Write $\sum\limits_{n=0}^\infty e^{-xn^3}$ in the form $\sum\limits_{n=-\infty}^\infty a_nx^n$

4 votes
2 answers
411 views

Alternative analytic continuation to zeta, not giving $-\frac{1}{12}$ for sum of integers

4 votes
2 answers
199 views

Whispering wall function

4 votes
1 answer
994 views

Shape of spectrum of bounded linear operator on complex Banach space

3 votes
2 answers
209 views

Criteria for formally derived Euler-Maclaurin-type formula

3 votes
0 answers
95 views

Pass 3D shape through hole in scaled copy of itself

3 votes
1 answer
73 views

For what $d$ does $\sum\limits_{m=-\infty}^{\infty}\int_0^\infty e^{-t}\left[I_{|m|}\left(\frac{t}{d}\right)\right]^d \;\mathrm dt$ converge?

3 votes
1 answer
338 views

Proof of Ramanujan doubly exponential series identity

3 votes
2 answers
204 views

Chaitin's constant and coding undecidable propositions in a number

3 votes
1 answer
73 views

Solving trigonometric equations like $1-s\sin^2\theta=a\sin^6\theta+b\cos^6\theta$