Mathematics
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Sangchul Lee
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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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All Questions Answers
Score Newest
answer
207
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, 2013
question
191
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, 2013
answer
181
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, 2013
answer
159
Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$
Jun 19, 2012
answer
121
Prove that $\frac{100!}{50!\cdot2^{50}} \in \Bbb{Z}$
Jul 7, 2013
answer
106
How can a "proper" function have a vertical slope?
Oct 5, 2019
answer
77
Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$
Feb 17, 2012
question
69
How much does symbolic integration mean to mathematics?
May 11, 2011
answer
63
How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$
May 1, 2012
answer
56
All real numbers in $[0,2]$ can be represented as $\sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \dots}}}$
Apr 6, 2016
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Does $a_n=\prod^n_{k=1}(1-e^{k\alpha \pi i})$ converge to zero when $\alpha$ is irrational?
12
Can a pronoun and its referent have different plurality?
8
Question about words ending with '-dle'
6
Redefining environment within a macro
5
Is there any known construction of IIC as a limit from supercritical phase?

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