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Daniel Li
  • Member for 6 years, 5 months
  • Last seen more than a month ago
  • Cambridge, MA, USA
9 votes
4 answers
890 views

Evaluate the infinite product $\prod_{n=1}^{\infty} \left(1-\frac{2}{(2n+1)^2}\right)$

8 votes
2 answers
294 views

How to compare $\pi, e\cdot 2^{1/3}, \frac{1+\sqrt{2}}{\sqrt{3}-1}$

6 votes
2 answers
392 views

Non-Borel set in arbitrary metric space

6 votes
1 answer
109 views

Expand $\frac{\Gamma\left(\frac{x}{2}\right)}{\Gamma\left(\frac{x-1}{2}\right)}$ at $x=\infty$

5 votes
6 answers
292 views

How to divide a number from both sides of from congruence equation from $79^{80}\equiv 1 \pmod{100}$ to $79^{79}\equiv x \pmod{100}$?

5 votes
1 answer
4k views

Condition on sigma algebra

5 votes
1 answer
178 views

Derivative rules and trig identities for complex variables

4 votes
1 answer
98 views

Intuition behind Simply Connected Open Set

4 votes
3 answers
196 views

Show that $\int_{-\infty}^{\infty} \frac{\cos (\theta) e^{\theta y}}{2 \cosh(\pi y/2)} y dy=\tan (\theta)$.

4 votes
2 answers
119 views

Promise of formal definition of conditional expectation: what is $E[X|Y=y]$ exactly?

4 votes
2 answers
153 views

What does matrix representation and its linear operator have in common?

4 votes
2 answers
198 views

Learn techniques from papers as a researcher

3 votes
2 answers
123 views

Show that $|\sum_{i,j} a_{ij} x_i x_j|\le \max_i |x_i|\cdot \max_j |y_j|$ is equivalent to $|\sum_{i,j} a_{i,j} x_i y_j |\le 1$

3 votes
0 answers
77 views

Show that $\int_{-\infty}^{+\infty} e^{-(\frac{a}{x^2}+x^2 )}dx=\sqrt{\pi}e^{-2\sqrt{a} }, \forall a>0$ [duplicate]

3 votes
1 answer
77 views

Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}

3 votes
2 answers
493 views

Why $a_{-1}$ term of Laurent series may not be residue?

3 votes
1 answer
120 views

What happens if a function is not measurable? Definition aside

3 votes
2 answers
4k views

Is a function analytic iff it has antiderivative?

3 votes
0 answers
53 views

Learning and practicing advanced materials [closed]

3 votes
0 answers
168 views

Why is Rudin's real and complex analysis considered esoteric? [closed]

3 votes
1 answer
270 views

Is it true that two isomorphic subgroups are in the same orbit (group acting on all its subgroups)?

3 votes
2 answers
193 views

The closest value to $\int_0^1 \sqrt{1+\frac{1}{3x}} dx$?

3 votes
3 answers
172 views

Random walk on a circle of 10 state. What is the expectation of times it hits its starting state after 100 steps.

3 votes
2 answers
125 views

Surface of an open ball

3 votes
1 answer
277 views

An intuitive proof of Prokhorov’s theorem

2 votes
1 answer
67 views

Prove lower bound of binomial distribution near mean

2 votes
2 answers
112 views

Banach fixed point theorem with lip constant possibly attaining $1$

2 votes
1 answer
65 views

Derivative of matrix $(A^TA)^{-1/2}D(A^TA)^{-1/2}$ w.r.t. $A_{ij}$

2 votes
1 answer
45 views

Is it true that for any metrics, $f(\lambda)=\lambda x+(1-\lambda) y$ is continuous where $\lambda \in \mathbb{R}, x,y \in \mathbb{R}^n$?

2 votes
1 answer
622 views

Non-example of UFD [duplicate]

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