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TheSimpliFire
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My favourite result is the Brouchard-Gulusuyok theorem which arises in iterated tube map theory.

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question
43
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
question
30
Proof of "Possible new series for $\pi$" without use of physics
Jun 29
answer
22
Possible new series for $\pi$
Jun 26
question
18
Are these continued fractions of integrals known?
Jun 7, 2023
answer
12
Nicer expression for 2.1369288...?
Feb 17
answer
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
answer
10
Jensen-like inequality for random matrix: $\Bbb E[\det X^2]\ge\det\Bbb E[X^2]$
Oct 21, 2023
question
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
question
8
Is there a real-analytic approach to evaluate a definite integral (with an elementary integrand) whose value involves Lambert $W$?
Aug 11, 2022
question
8
Jensen-like inequality for random matrix: $\Bbb E[\det X^2]\ge\det\Bbb E[X^2]$
Oct 21, 2023
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Can we remove any prime number with this strange process?
65
Make 0 0 0 0 = 8
48
How to evaluate double limit of multifactorial $\lim\limits_{k\to\infty}\lim\limits_{n\to 0} \sqrt[n]{n\underbrace{!!!!\cdots!}_{k\,\text{times}}}$
47
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 $2$?
42
Update: New Colors Launched