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Sasha's user avatar
Sasha's user avatar
Sasha
  • Member for 13 years, 1 month
  • Last seen more than a week ago
78 votes
Accepted

Modular exponentiation by hand ($a^b\bmod c$)

75 votes
Accepted

Expectation of the maximum of gaussian random variables

70 votes
Accepted

Lebesgue measurable set that is not a Borel measurable set

67 votes

Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$

62 votes

Why is $\Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}$?

55 votes
Accepted

Is the integral $\int_0^\infty \frac{\mathrm{d} x}{(1+x^2)(1+x^a)}$ equal for all $a \neq 0$?

49 votes
Accepted

Calculation of the n-th central moment of the normal distribution $\mathcal{N}(\mu,\sigma^2)$

46 votes
Accepted

Characteristic function of a standard normal random variable

43 votes
Accepted

Prove elementarily that $\sqrt[n+1] {(n+1)!} - \sqrt[n] {n!}$ is strictly decreasing

41 votes

Math and mental fatigue

40 votes
Accepted

Proof that the hypergeometric distribution with large $N$ approaches the binomial distribution.

36 votes

Symmetry of function defined by integral

36 votes
Accepted

Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$

35 votes

Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$

35 votes
Accepted

Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?

34 votes

How to sum this series for $\pi/2$ directly?

33 votes
Accepted

Proving $ \int_{0}^{\infty} \frac{\ln(t)}{\sqrt{t}}e^{-t} \mathrm dt=-\sqrt{\pi}(\gamma+\ln{4})$

30 votes
Accepted

Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$

30 votes
Accepted

Help me evaluate $\int_0^1 \frac{\log(x+1)}{1+x^2} dx$

29 votes
Accepted

A curious limit for $-\frac{\pi}{2}$

28 votes

How to prove that geometric distributions converge to an exponential distribution?

26 votes
Accepted

Indefinite Integral of $\sqrt{\sin x}$

25 votes

Root Calculation by Hand

25 votes
Accepted

Distribution of hitting time of line by Brownian motion

24 votes

integrate square of $\arctan x$. Tricky

24 votes

Evaluating $\int_0^{\frac\pi2}\frac{\ln{(\sin x)}\ \ln{(\cos x})}{\tan x}\ dx$

23 votes

Random point uniform on a sphere

22 votes

What is the correct inter-arrival time distribution in a Poisson process?

22 votes
Accepted

Evaluation of $\sum\limits_{n=0}^\infty \left(\operatorname{Si}(n)-\frac{\pi}{2}\right)$?

22 votes
Accepted

Calculate sum of $\sum_{n=1}^{\infty}(-1)^n\frac{\ln n}{n}$

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