User Daniel Li

9 votes

4 answers

890 views

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

asked Sep 24, 2017 at 22:19

8 votes

2 answers

294 views

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

calculus algebra-precalculus approximation

asked Aug 26, 2019 at 2:31

6 votes

2 answers

392 views

Non-Borel set in arbitrary metric space

real-analysis general-topology functional-analysis measure-theory

asked Mar 19, 2019 at 23:34

6 votes

1 answer

109 views

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

calculus sequences-and-series taylor-expansion gamma-function laurent-series

asked Feb 7, 2021 at 18:25

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 $79^{79}\equiv x \pmod{100}$?

abstract-algebra number-theory modular-arithmetic

asked Aug 16, 2019 at 15:38

5 votes

1 answer

4k views

Condition on sigma algebra

probability probability-theory measure-theory

asked Jul 27, 2017 at 2:56

5 votes

1 answer

178 views

Derivative rules and trig identities for complex variables

complex-analysis complex-numbers

asked Feb 7, 2018 at 16:22

4 votes

1 answer

98 views

Intuition behind Simply Connected Open Set

calculus complex-analysis intuition

asked Aug 29, 2017 at 18:50

4 votes

3 answers

196 views

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

calculus integration analysis definite-integrals

asked Feb 4, 2019 at 3:19

4 votes

2 answers

119 views

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

real-analysis probability

asked Feb 19, 2019 at 4:23

4 votes

2 answers

153 views

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

linear-algebra big-list

asked Jul 26, 2019 at 2:51

4 votes

2 answers

198 views

Learn techniques from papers as a researcher

soft-question

asked Feb 2, 2020 at 22:47

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 $|\sum_{i,j} a_{i,j} x_i y_j |\le 1$

inequality

asked Jun 28, 2020 at 3:55

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]

integration complex-analysis

asked Oct 10, 2020 at 5:12

3 votes

1 answer

77 views

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

real-analysis functional-analysis lipschitz-functions

asked Mar 21, 2019 at 15:39

3 votes

2 answers

493 views

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

complex-analysis complex-numbers laurent-series

asked Aug 12, 2019 at 23:46

3 votes

1 answer

120 views

What happens if a function is not measurable? Definition aside

real-analysis probability measure-theory

asked Jul 25, 2017 at 22:22

3 votes

2 answers

4k views

Is a function analytic iff it has antiderivative?

calculus complex-analysis analytic-functions

asked Jul 26, 2017 at 17:36

3 votes

0 answers

53 views

Learning and practicing advanced materials [closed]

soft-question

asked Feb 9, 2018 at 19:45

3 votes

0 answers

168 views

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

soft-question

asked May 10, 2018 at 20:39

3 votes

1 answer

270 views

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

abstract-algebra group-theory

asked Oct 2, 2018 at 2:57

3 votes

2 answers

193 views

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

calculus integration definite-integrals

asked Jan 15, 2019 at 12:41

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.

probability combinatorics

asked Jan 24, 2019 at 18:55

3 votes

2 answers

125 views

Surface of an open ball

real-analysis general-topology analysis

asked Jan 30, 2019 at 0:27

3 votes

1 answer

277 views

An intuitive proof of Prokhorov’s theorem

real-analysis probability-theory measure-theory stochastic-processes

asked Sep 17, 2020 at 3:29

2 votes

1 answer

67 views

Prove lower bound of binomial distribution near mean

probability combinatorics statistics binomial-distribution

asked Dec 23, 2020 at 23:58

2 votes

2 answers

112 views

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

real-analysis functional-analysis

asked Jan 2, 2021 at 0:30

2 votes

1 answer

65 views

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

matrix-calculus

asked Jun 11, 2021 at 22:54

2 votes

1 answer

45 views

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

real-analysis general-topology analysis

asked Jan 27, 2019 at 18:52

2 votes

1 answer

622 views

Non-example of UFD [duplicate]

abstract-algebra ring-theory examples-counterexamples factoring

asked Dec 5, 2018 at 19:06

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158 Questions

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

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

Non-Borel set in arbitrary metric space

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

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

Condition on sigma algebra

Derivative rules and trig identities for complex variables

Intuition behind Simply Connected Open Set

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

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

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

Learn techniques from papers as a researcher

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

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

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

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

What happens if a function is not measurable? Definition aside

Is a function analytic iff it has antiderivative?

Learning and practicing advanced materials [closed]

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

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

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

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

Surface of an open ball

An intuitive proof of Prokhorov’s theorem

Prove lower bound of binomial distribution near mean

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

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

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

Non-example of UFD [duplicate]