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TheSimpliFire
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63
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?
Feb 26, 2022
32
Proof of "Possible new series for $\pi$" without use of physics
Jun 29, 2024
23
Possible new series for $\pi$
Jun 26, 2024
18
Are these continued fractions of integrals known?
Jun 7, 2023
12
Nicer expression for 2.1369288...?
Feb 17, 2024
11
Find the area of the region enclosed by $\frac{\sin x}{\sin y}=\frac{\sin x+\sin y}{\sin(x+y)}$ and the $x$-axis (comes from a probability question)
Apr 19, 2024
10
Jensen-like inequality for random matrix: $\Bbb E[\det X^2]\ge\det\Bbb E[X^2]$
Oct 21, 2023
9
Is $(m,n)=(2,3)$ the only solution to $\sum_\limits{k \in\Bbb Z}\frac1{(W_k(x)+1)^m}=\sum_\limits{k \in\Bbb Z}\frac1{(W_k(x)+1)^n}$?
Jan 24, 2023
9
Jensen-like inequality for random matrix: $\Bbb E[\det X^2]\ge\det\Bbb E[X^2]$
Oct 21, 2023
8
Is there a real-analytic approach to evaluate a definite integral (with an elementary integrand) whose value involves Lambert $W$?
Aug 11, 2022

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110
Can we remove any prime number with this strange process?
52
How to evaluate double limit of multifactorial $\lim\limits_{k\to\infty}\lim\limits_{n\to 0} \sqrt[n]{n\underbrace{!!!!\cdots!}_{k\,\text{times}}}$
50
Is each of $\int_0^\infty\frac{dx}{x^x},\int_0^\infty\frac{dx}{x^{x^{x^x}}},\int_0^\infty\frac{dx}{x^{x^{x^{x^{x^x}}}}},\cdots$ less than $2$?