Sasha
Reputation
52,043
89/100 score
4 72 141
Impact
~831k people reached

 48 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 30 Symmetry of function defined by integral 30 Expectation of the maximum of gaussian random variables 30 Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$

### Reputation (52,043)

 +25 Solving a SDE / Finding expectation Value +10 Proof that the hypergeometric distribution with large $N$ approaches the binomial distribution. +10 Help me evaluate $\int_0^1 \frac{\log(x+1)}{1+x^2} dx$ +10 How to get closed form from generating function?

### Questions (38)

 38 Probability for the length of the longest run in $n$ Bernoulli trials 14 How does one prove $\int_0^\infty \prod_{k=1}^\infty \operatorname{\rm sinc}\left( \frac{t}{2^{k+1}} \right) \mathrm{d} t = 2 \pi$ 13 Large $n$ asymptotic of $\int_0^\infty \left( 1 + x/n\right)^{n-1} \exp(-x) \, \mathrm{d} x$ 12 Detecting symmetric matrices of the form (low-rank + diagonal matrix) 12 Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly

### Tags (237)

 1k calculus × 168 313 probability-distributions × 126 958 integration × 158 308 special-functions × 68 792 probability × 310 293 definite-integrals × 49 517 sequences-and-series × 92 232 statistics × 96 315 real-analysis × 50 201 combinatorics × 57

### Accounts (14)

 Mathematics 52,043 rep 472141 Stack Overflow 5,443 rep 11329 Mathematica 5,226 rep 1736 Cross Validated 265 rep 39 Area 51 236 rep 4