TheSimpliFire

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Answers

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Score Activity Newest

30

Let $A=(a_{ij})$ be an $n\times n$ matrix. Suppose that $A^2$ is diagonal. Must $A$ be diagonal?

Apr 12, 2018

20

Why is $\sum\limits_{n=1}^{\infty}e^{-(n/10)^2}$ almost equal to $5\sqrt\pi-\frac12$ (agreeing up to $427$ digits)?

Nov 7, 2020

19

Does there exist a real function with domain $\Bbb{R}$ such that $f'(x)>0$ and $f''(x)+(f'(x))^2<0$ for all $x$?

Jul 3, 2021

18

Is this a new characteristic function for the primes?

Oct 12, 2019

16

Evaluating $\int_0^1\frac{3x^4+ 4x^3 + 3x^2}{(4x^3 + 3x^2 + 2x+ 1)^2}\, dx$

Jul 5, 2018

Questions

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106

Can we remove any prime number with this strange process?

Jul 8, 2019

47

How to evaluate double limit of multifactorial $\lim\limits_{k\to\infty}\lim\limits_{n\to 0} \sqrt[n]{n\underbrace{!!!!\cdots!}_{k\,\text{times}}}$

Feb 18, 2021

44

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 $2$?

Feb 15, 2022

36

Is $100$ the only square number of the form $a^b+b^a$?

Jul 14, 2019

34

Are these continued fractions of integrals known?

Jul 6, 2019

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+10

What is the purpose of $\frac{1}{\sigma \sqrt{2 \pi}}$ in $\frac{1}{\sigma \sqrt{2 \pi}}e^{\frac{(-(x - \mu ))^2}{2\sigma ^2}}$?

+10

How to evaluate the limit of multifactorial $\lim_{n\to 0} \sqrt[n]{n!!!!\cdots !}$

+10

Examples of integration by parts that work both ways

+10

How to evaluate double limit of multifactorial $\lim\limits_{k\to\infty}\lim\limits_{n\to 0} \sqrt[n]{n\underbrace{!!!!\cdots!}_{k\,\text{times}}}$

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