User TheSimpliFire

43 votes

1 answer

2k views

Is $\int_0^\infty{dx\over x^{x^{x^x}}}<\int_0^\infty{dx\over x^{x^{x^{x^{x^x}}}}}<\int_0^\infty{dx\over x^{x^{x^{x^{x^{x^{x^x}}}}}}}<\cdots$ true?

asked Feb 26, 2022 at 14:40

30 votes

1 answer

4k views

Proof of "Possible new series for $\pi$" without use of physics

asked Jun 29 at 0:39

18 votes

0 answers

718 views

Are these continued fractions of integrals known?

asked Jun 7, 2023 at 18:04

9 votes

1 answer

222 views

Is $(m,n)=(2,3)$ the only solution to $\sum_\limits{k \in\Bbb Z}\frac1{(W_k(x)+1)^m}=\sum_\limits{k \in\Bbb Z}\frac1{(W_k(x)+1)^n}$?

asked Jan 24, 2023 at 17:21

8 votes

3 answers

595 views

Jensen-like inequality for random matrix: $\Bbb E[\det X^2]\ge\det\Bbb E[X^2]$

asked Oct 21, 2023 at 0:15

8 votes

0 answers

296 views

Is there a real-analytic approach to evaluate a definite integral (with an elementary integrand) whose value involves Lambert $W$?

asked Aug 11, 2022 at 10:56

7 votes

2 answers

291 views

Signs of Kravchuk matrix asymptotically produce a large circular region with hyperbolic sinks. Why?

asked Feb 16, 2023 at 1:37

5 votes

1 answer

358 views

Is there a meaningful interpretation of an $L^i$-space?

asked Jun 16, 2023 at 17:58

4 votes

1 answer

109 views

Dividing a spherical cap into three equal wedges

asked Dec 27, 2022 at 18:42

4 votes

1 answer

183 views

Maximal increasing behaviour of $\sqrt{-\log x}\operatorname{Li}_{1/2}(x)$

asked Dec 21, 2021 at 12:36

3 votes

1 answer

245 views

Dividing a spherical cap into $n$ equal wedges

asked Dec 27, 2022 at 21:23

3 votes

1 answer

83 views

Curious asymptotics of real part of ratio between Lambert W branches

asked Jun 11 at 19:31

3 votes

1 answer

340 views

Proof of continued fraction identity of subfactorial

asked Apr 30, 2020 at 13:48

2 votes

1 answer

240 views

Bounds on largest possible square in sum of two squares

asked May 17, 2022 at 14:40

1 vote

1 answer

75 views

Does a minimiser exist for this Gaussian-like functional?

asked Feb 15, 2022 at 22:04

1 vote

1 answer

248 views

On finding the critical points of $f(x)=\left(x-a+\frac1{ax}\right)^a-\left(\frac1x-\frac1a+ax\right)^x$

asked Jun 5, 2018 at 18:52

1 vote

1 answer

121 views

On the regularity of integer solutions of a simultaneous equation with consecutive prime coefficients

asked Jun 6, 2018 at 14:22

1 vote

1 answer

127 views

Does the intercept converge if we fit a best fit line to points with prime coordinates?

asked Mar 31, 2019 at 16:00

0 votes

1 answer

161 views

Analogues of Kac-Bernstein characterisation theorem for non-normal distributions

asked Mar 17, 2023 at 1:25

0 votes

0 answers

60 views

Existence of integer sequence under simultaneous constraints

asked May 10, 2023 at 22:08

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20 Questions

Is $\int_0^\infty{dx\over x^{x^{x^x}}}<\int_0^\infty{dx\over x^{x^{x^{x^{x^x}}}}}<\int_0^\infty{dx\over x^{x^{x^{x^{x^{x^{x^x}}}}}}}<\cdots$ true?

Proof of "Possible new series for $\pi$" without use of physics

Are these continued fractions of integrals known?

Is $(m,n)=(2,3)$ the only solution to $\sum_\limits{k \in\Bbb Z}\frac1{(W_k(x)+1)^m}=\sum_\limits{k \in\Bbb Z}\frac1{(W_k(x)+1)^n}$?

Jensen-like inequality for random matrix: $\Bbb E[\det X^2]\ge\det\Bbb E[X^2]$

Is there a real-analytic approach to evaluate a definite integral (with an elementary integrand) whose value involves Lambert $W$?

Signs of Kravchuk matrix asymptotically produce a large circular region with hyperbolic sinks. Why?

Is there a meaningful interpretation of an $L^i$-space?

Dividing a spherical cap into three equal wedges

Maximal increasing behaviour of $\sqrt{-\log x}\operatorname{Li}_{1/2}(x)$

Dividing a spherical cap into $n$ equal wedges

Curious asymptotics of real part of ratio between Lambert W branches

Proof of continued fraction identity of subfactorial

Bounds on largest possible square in sum of two squares

Does a minimiser exist for this Gaussian-like functional?

On finding the critical points of $f(x)=\left(x-a+\frac1{ax}\right)^a-\left(\frac1x-\frac1a+ax\right)^x$

On the regularity of integer solutions of a simultaneous equation with consecutive prime coefficients

Does the intercept converge if we fit a best fit line to points with prime coordinates?

Analogues of Kac-Bernstein characterisation theorem for non-normal distributions

Existence of integer sequence under simultaneous constraints