User Yuriy S

68 votes

Conjectures that have been disproved with extremely large counterexamples?

answered Aug 4, 2016 at 7:15

34 votes

Accepted

Why is this trigonometric identity true?

answered Nov 11, 2016 at 11:35

22 votes

Is there any integral for the Golden Ratio?

answered Feb 14, 2016 at 3:48

20 votes

Dog bone-shaped curve: $|x|^x=|y|^y$

answered Feb 17, 2018 at 11:49

20 votes

Number of equations needed to define a rectangle?

answered Oct 29, 2018 at 18:54

18 votes

Is there any integral for the Golden Ratio?

answered Apr 11, 2016 at 12:47

14 votes

Accepted

Is $0.248163264128…$ a transcendental number?

answered Feb 18, 2016 at 10:48

11 votes

Crazy pattern in the simple continued fraction for $\sum_{k=1}^\infty \frac{1}{(2^k)!}$

answered Aug 29, 2016 at 17:49

11 votes

Accepted

What is the general solution of a multivariate quadratic equation

answered Jul 27, 2016 at 18:49

11 votes

Euler-Mascheroni constant in Bessel function integral

answered Jun 10, 2022 at 10:53

11 votes

Accepted

What does $\sum_{n=1}^\infty\frac{1}{\sqrt n(n+1)}$ converge to exactly?

answered Nov 2, 2018 at 20:39

11 votes

Does it make sense to learn mathematical concepts as you encounter them rather than in a fixed progression?

answered Dec 24, 2018 at 7:48

10 votes

Calculate the determinant $\left|\begin{smallmatrix} a&b&c&d\\ b&a&d&c\\ c&d&a&b\\d&c&b&a\end{smallmatrix}\right|$

answered Feb 12, 2018 at 9:50

9 votes

Visual representation of the fact that there are more irrational than rational numbers.

answered Jun 15, 2016 at 18:58

9 votes

Prove $\int_0^{\pi/2}{\frac{1+2\cos 2x\cdot\ln\tan x}{1+\tan^{2\sqrt{2}} x}}\tan^{1/\sqrt{2}} x~dx=0$

answered Jan 10, 2017 at 19:44

9 votes

Accepted

Infinite series with harmonic numbers related to elliptic integrals

answered Feb 2, 2018 at 10:36

8 votes

Tough integrals that can be easily beaten by using simple techniques

answered Jun 10, 2016 at 20:30

8 votes

Is there any integral for the Golden Ratio?

answered Jun 13, 2016 at 18:45

8 votes

Closed-form of log gamma integral $\int_0^z\ln\Gamma(t)~dt$ for $z =1,\frac12, \frac13, \frac14, \frac16,$ using Catalan's and Gieseking's constant?

answered Jul 26, 2019 at 20:40

7 votes

Nested Radicals and Continued Fractions

answered Feb 21, 2016 at 1:04

7 votes

Evaluate the infinite product $\prod_{k \geq 2}\sqrt[k]{1+\frac{1}{k}}=\sqrt{1+\frac{1}{2}} \sqrt[3]{1+\frac{1}{3}} \sqrt[4]{1+\frac{1}{4}} \cdots$

answered Feb 22, 2016 at 4:10

7 votes

Convergent sequence of irrational numbers that has a rational limit.

answered Feb 12, 2016 at 23:28

7 votes

Behavior of Pascal's triangle in $n\mod m$ where $m>2$, any fractals?

answered Sep 14, 2016 at 19:47

7 votes

Convergence of a Harmonic Continued Fraction

answered Jul 26, 2016 at 16:26

7 votes

An integral inequality (one variable)

answered Feb 8, 2018 at 21:25

7 votes

The limit $\lim_{r\to0}\frac1r\left(1-\binom{n}{r}^{-1}\right)$

answered Aug 3, 2019 at 23:58

7 votes

A series for $\log (a) \log (b)$ in terms of hypergeometric function

answered Jul 19, 2019 at 21:56

6 votes

What is $\int_0^1 \ln (1-x) \ln \left(\ln \left(\frac{1}{x}\right)\right) \, dx$?

answered Apr 8, 2016 at 21:30

6 votes

Integral $\int_{-\infty}^\infty\frac{\Gamma(x)\,\sin(\pi x)}{\Gamma\left(x+a\right)}\,dx$

answered Jun 9, 2016 at 16:17

6 votes

Accepted

Limit of $\ln(1\cdot\ln(2\cdot\ln(3\cdot\ln(4\cdots))))$

answered Feb 8, 2016 at 14:12

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509 Answers

Conjectures that have been disproved with extremely large counterexamples?

Why is this trigonometric identity true?

Is there any integral for the Golden Ratio?

Dog bone-shaped curve: $|x|^x=|y|^y$

Number of equations needed to define a rectangle?

Is there any integral for the Golden Ratio?

Is $0.248163264128…$ a transcendental number?

Crazy pattern in the simple continued fraction for $\sum_{k=1}^\infty \frac{1}{(2^k)!}$

What is the general solution of a multivariate quadratic equation

Euler-Mascheroni constant in Bessel function integral

What does $\sum_{n=1}^\infty\frac{1}{\sqrt n(n+1)}$ converge to exactly?

Does it make sense to learn mathematical concepts as you encounter them rather than in a fixed progression?

Calculate the determinant $\left|\begin{smallmatrix} a&b&c&d\\ b&a&d&c\\ c&d&a&b\\d&c&b&a\end{smallmatrix}\right|$

Visual representation of the fact that there are more irrational than rational numbers.

Prove $\int_0^{\pi/2}{\frac{1+2\cos 2x\cdot\ln\tan x}{1+\tan^{2\sqrt{2}} x}}\tan^{1/\sqrt{2}} x~dx=0$

Infinite series with harmonic numbers related to elliptic integrals

Tough integrals that can be easily beaten by using simple techniques

Is there any integral for the Golden Ratio?

Closed-form of log gamma integral $\int_0^z\ln\Gamma(t)~dt$ for $z =1,\frac12, \frac13, \frac14, \frac16,$ using Catalan's and Gieseking's constant?

Nested Radicals and Continued Fractions

Evaluate the infinite product $\prod_{k \geq 2}\sqrt[k]{1+\frac{1}{k}}=\sqrt{1+\frac{1}{2}} \sqrt[3]{1+\frac{1}{3}} \sqrt[4]{1+\frac{1}{4}} \cdots$

Convergent sequence of irrational numbers that has a rational limit.

Behavior of Pascal's triangle in $n\mod m$ where $m>2$, any fractals?

Convergence of a Harmonic Continued Fraction

An integral inequality (one variable)

The limit $\lim_{r\to0}\frac1r\left(1-\binom{n}{r}^{-1}\right)$

A series for $\log (a) \log (b)$ in terms of hypergeometric function

What is $\int_0^1 \ln (1-x) \ln \left(\ln \left(\frac{1}{x}\right)\right) \, dx$?

Integral $\int_{-\infty}^\infty\frac{\Gamma(x)\,\sin(\pi x)}{\Gamma\left(x+a\right)}\,dx$

Limit of $\ln(1\cdot\ln(2\cdot\ln(3\cdot\ln(4\cdots))))$