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Sangchul Lee

I received my PhD at University of California, Los Angeles. 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?

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205 A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$ Oct 12 '13
189 Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$ Nov 25 '13
176 Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$ Nov 17 '13
157 Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ Jun 19 '12
120 Prove that $\frac{100!}{50!\cdot2^{50}} \in \Bbb{Z}$ Jul 7 '13
105 How can a “proper” function have a vertical slope? Oct 5 '19
73 Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$ Feb 17 '12
68 How much does symbolic integration mean to mathematics? May 11 '11
64 How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$ May 1 '12
57 An integral involving Fresnel integrals $\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm dx,$ May 23 '13
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