 # Sangchul Lee

Los Angeles, CA, USA

http://sos440.blogspot.kr/

I am currently interested in probability theory and analytic combinatorics. Here is a selection of my answers:

Limiting distribution of $$\frac{1}{n} \sum_{k=1}^{n}|S_{k-1}|(X_k^2 - 1)$$, where $$X_k$$ are i.i.d. standard normal

Does the sum $$\sum_{n \geq 1} \frac{2^n\text{ mod } n}{n^2}$$ converge?

Expected absolute difference between two i.i.d. variables

Does the sequence $$x_{n+1} = -16 + 6x_n + \frac{12}{x_n}$$ converge?

Proving $$\lim_{x \to 0+} \sum_{n=0}^\infty (-1)^n/(n!)^x = \frac{1}{2}$$

Solution of the functional equation $$f(x) + f(y) = f(x + y + 2f(xy))$$

How to prove the existence of this limit?

Top Questions

## Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$

asked Nov 25, 2013 at 12:51

## How much does symbolic integration mean to mathematics?

asked May 11, 2011 at 15:25

## Integral $\int_{-1}^{1} \frac{1}{x}\sqrt{\frac{1+x}{1-x}} \log \left( \frac{(r-1)x^{2} + sx + 1}{(r-1)x^{2} - sx + 1} \right) \, \mathrm dx$

asked Nov 16, 2013 at 1:48

## Extending the result $\int_{0}^{\infty} \left( ( 1 - 2C(x))^{2} + (1-2S(x))^{2} \right) \, dx = \frac{4}{\pi}$

asked May 25, 2013 at 15:06

## Polynomial equations $p(A, B) = 0$ for matrices that ensure $AB = BA$

asked Jul 30, 2011 at 20:53

## Patterns of the zeros of the Faulhaber polynomials (modified)

asked Mar 1, 2013 at 0:58

## References to integrals of the form $\int_{0}^{1} \left( \frac{1}{\log x}+\frac{1}{1-x} \right)^{m} \, dx$

asked Mar 25, 2013 at 15:17