User Daniel Li

9 votes

4 answers

899 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

299 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

395 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

4k views

Condition on sigma algebra

probability probability-theory measure-theory

asked Jul 27, 2017 at 2:56

6 votes

1 answer

110 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

1 answer

187 views

Derivative rules and trig identities for complex variables

complex-analysis complex-numbers

asked Feb 7, 2018 at 16:22

5 votes

6 answers

308 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

4 votes

3 answers

197 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

123 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

156 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

205 views

Learn techniques from papers as a researcher

soft-question

asked Feb 2, 2020 at 22:47

4 votes

1 answer

99 views

Intuition behind Simply Connected Open Set

calculus complex-analysis intuition

asked Aug 29, 2017 at 18:50

3 votes

1 answer

121 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

2 answers

3k views

What is a countably generated $\sigma$-algebra? Can't find a definition online [closed]

probability general-topology measure-theory

asked Oct 3, 2017 at 21:24

3 votes

0 answers

54 views

Learning and practicing advanced materials [closed]

soft-question

asked Feb 9, 2018 at 19:45

3 votes

0 answers

169 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

210 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

174 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

131 views

Surface of an open ball

real-analysis general-topology analysis

asked Jan 30, 2019 at 0:27

3 votes

2 answers

129 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

78 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

510 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

295 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

71 views

Prove lower bound of binomial distribution near mean

probability combinatorics statistics binomial-distribution

asked Dec 23, 2020 at 23:58

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

2 answers

117 views

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

real-analysis functional-analysis

asked Jan 2, 2021 at 0:30

2 votes

0 answers

169 views

Prove $(1-a)^2+(1-b)^2+(1-c)^2 \ge \frac{c^2(1-a^2)(1-b^2)}{(ab+c)^2}+\frac{b^2(1-a^2)(1-c^2)}{(ac+b)^2}+\frac{a^2(1-c^2)(1-b^2)}{(bc+a)^2}$ [duplicate]

inequality

asked Aug 18, 2019 at 14:51

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157 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

Condition on sigma algebra

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

Derivative rules and trig identities for complex variables

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

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

Intuition behind Simply Connected Open Set

What happens if a function is not measurable? Definition aside

Is a function analytic iff it has antiderivative?

What is a countably generated $\sigma$-algebra? Can't find a definition online [closed]

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

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?

An intuitive proof of Prokhorov’s theorem

Prove lower bound of binomial distribution near mean

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

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

Prove $(1-a)^2+(1-b)^2+(1-c)^2 \ge \frac{c^2(1-a^2)(1-b^2)}{(ab+c)^2}+\frac{b^2(1-a^2)(1-c^2)}{(ac+b)^2}+\frac{a^2(1-c^2)(1-b^2)}{(bc+a)^2}$ [duplicate]