User Anon

52 votes

2 answers

5k views

Why can't Antoine's necklace fall apart?

asked Apr 21, 2020 at 6:31

25 votes

3 answers

849 views

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

calculus definite-integrals closed-form gamma-function elliptic-integrals

asked Jan 21, 2017 at 5:51

20 votes

4 answers

2k views

Rational function approximation to square root

real-analysis algebra-precalculus binomial-coefficients approximation elementary-functions

asked Oct 25, 2016 at 4:16

14 votes

1 answer

352 views

How do we know we get the right answer?

soft-question computability philosophy

asked Jan 31, 2017 at 6:29

12 votes

2 answers

356 views

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

integration multivariable-calculus definite-integrals closed-form

asked Feb 2, 2017 at 6:48

12 votes

2 answers

236 views

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

definite-integrals closed-form gamma-function bessel-functions elliptic-integrals

asked Jan 23, 2017 at 5:48

11 votes

0 answers

714 views

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

complex-analysis number-theory prime-numbers analytic-number-theory riemann-zeta

asked Jan 14, 2017 at 4:31

9 votes

1 answer

299 views

How are Trott constants found; are there mathematical results?

recreational-mathematics continued-fractions decimal-expansion constants experimental-mathematics

asked Jan 20, 2017 at 23:56

8 votes

1 answer

234 views

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

sequences-and-series convergence-divergence recreational-mathematics constants

asked Feb 3, 2017 at 5:22

8 votes

1 answer

316 views

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

calculus sequences-and-series laplace-transform bessel-functions elliptic-integrals

asked Dec 1, 2016 at 2:24

7 votes

1 answer

293 views

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

calculus sequences-and-series approximation bernoulli-numbers

asked Jan 9, 2017 at 6:29

7 votes

0 answers

344 views

Why does this fractal approximate so many others?

approximation fractals

asked Feb 6, 2017 at 7:16

7 votes

1 answer

341 views

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

integration definite-integrals closed-form gamma-function hypergeometric-function

asked Jan 29, 2017 at 6:11

7 votes

0 answers

179 views

Origami-constructible numbers

geometry recreational-mathematics geometric-construction origami

asked Apr 27, 2020 at 13:08

7 votes

0 answers

110 views

Explain approximate lines in graph of this function

sequences-and-series functions graphing-functions approximation decimal-expansion

asked Feb 22, 2017 at 6:39

6 votes

0 answers

148 views

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

sequences-and-series closed-form lambert-w

asked Feb 8, 2017 at 2:31

6 votes

0 answers

154 views

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

calculus real-analysis sequences-and-series laplace-transform riemann-zeta

asked Oct 29, 2016 at 0:07

5 votes

0 answers

159 views

Proportion of cube closer to centre than outside

integration geometry definite-integrals volume

asked Nov 11, 2016 at 6:40

5 votes

0 answers

262 views

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

probability combinatorics optimization

asked Dec 10, 2016 at 3:23

5 votes

1 answer

598 views

Series related to the Mandelbrot set

sequences-and-series polynomials convergence-divergence complex-numbers fractals

asked Dec 18, 2016 at 7:06

5 votes

2 answers

358 views

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

calculus sequences-and-series complex-analysis recreational-mathematics closed-form

asked Feb 1, 2017 at 6:54

4 votes

2 answers

411 views

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

sequences-and-series complex-analysis analytic-continuation

asked Nov 1, 2016 at 5:34

4 votes

2 answers

199 views

Whispering wall function

calculus geometry ordinary-differential-equations

asked Nov 9, 2016 at 6:32

4 votes

1 answer

994 views

Shape of spectrum of bounded linear operator on complex Banach space

complex-analysis functional-analysis operator-theory spectral-theory

asked Nov 10, 2016 at 23:52

3 votes

2 answers

209 views

Criteria for formally derived Euler-Maclaurin-type formula

calculus real-analysis sequences-and-series laplace-transform

asked Oct 28, 2016 at 2:38

3 votes

0 answers

95 views

Pass 3D shape through hole in scaled copy of itself

geometry optimization euclidean-geometry analytic-geometry

asked Jan 6, 2017 at 5:21

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?

calculus probability sequences-and-series convergence-divergence bessel-functions

asked Jan 8, 2017 at 23:39

3 votes

1 answer

338 views

Proof of Ramanujan doubly exponential series identity

sequences-and-series complex-analysis gamma-function fourier-transform

asked Nov 19, 2016 at 6:20

3 votes

2 answers

204 views

Chaitin's constant and coding undecidable propositions in a number

algorithms computability information-theory computational-mathematics turing-machines

asked Jan 25, 2017 at 23:57

3 votes

1 answer

73 views

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

trigonometry

asked Jan 22, 2017 at 23:40

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44 Questions

Why can't Antoine's necklace fall apart?

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

Rational function approximation to square root

How do we know we get the right answer?

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

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

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

How are Trott constants found; are there mathematical results?

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

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

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

Why does this fractal approximate so many others?

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

Origami-constructible numbers

Explain approximate lines in graph of this function

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

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

Proportion of cube closer to centre than outside

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

Series related to the Mandelbrot set

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

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

Whispering wall function

Shape of spectrum of bounded linear operator on complex Banach space

Criteria for formally derived Euler-Maclaurin-type formula

Pass 3D shape through hole in scaled copy of itself

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?

Proof of Ramanujan doubly exponential series identity

Chaitin's constant and coding undecidable propositions in a number

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