Sasha
Reputation
54,597
90/100 score
4 79 154
Impact
~1.1m people reached

 49 Is the integral $\int_0^\infty \frac{\mathrm{d} x}{(1+x^2)(1+x^a)}$ equal for all $a \neq 0$? 37 Prove elementarily that $\sqrt[n+1] {(n+1)!} - \sqrt[n] {n!}$ is strictly decreasing 34 Expectation of the maximum of gaussian random variables 34 Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$ 30 Symmetry of function defined by integral

### Reputation (54,597)

 +10 Expectation of the min of two independent random variables? +10 Evaluation of a trigonometric partial sum +10 Lebesgue measurable set that is not a Borel measurable set +10 How do I compute $a^b\,\bmod c$ by hand?

### Questions (39)

 41 Probability for the length of the longest run in $n$ Bernoulli trials 16 Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly 15 How does one prove $\int_0^\infty \prod_{k=1}^\infty \operatorname{\rm sinc}\left( \frac{t}{2^{k+1}} \right) \mathrm{d} t = 2 \pi$ 14 Large $n$ asymptotic of $\int_0^\infty \left( 1 + x/n\right)^{n-1} \exp(-x) \, \mathrm{d} x$ 13 Detecting symmetric matrices of the form (low-rank + diagonal matrix)

### Tags (246)

 1k calculus × 171 334 real-analysis × 50 1k integration × 161 326 special-functions × 68 848 probability × 317 311 definite-integrals × 51 534 sequences-and-series × 92 254 statistics × 97 347 probability-distributions × 130 202 combinatorics × 57

### Accounts (14)

 Mathematics 54,597 rep 479154 Mathematica 6,153 rep 2041 Stack Overflow 5,557 rep 11530 Cross Validated 320 rep 310 Area 51 236 rep 4