User Feng - Mathematics Stack Exchange

1. Home
2. Questions
3. Unanswered
4. AI Assist
5. Tags
7. Chat
8. Users
Stack Internal

Stack Overflow for Teams is now called Stack Internal. Bring the best of human thought and AI automation together at your work.
Try for free Learn more
Stack Internal
Bring the best of human thought and AI automation together at your work. Learn more

Feng

Member for 7 years, 4 months
Last seen more than a week ago

China

Summary

Reputation

13,978

14k
9.9k
5.8k

2023
2024
2025
2026

Next tag badge

370/400 score

127/80 answers

Badges

27

26

46

Newest

Yearling

Next badge

341/500

Copy Editor

Impact

~100k

people reached

565

helpful flags

1,298

votes cast

Answers

View all 315 answers

23

compute $\int_0^1\sqrt{x(1-x)}dx$.

Nov 16, 2022

22

How to show analytically that $x^4-4x^3-2x^2+16x+24=0$ has no solutions in $\mathbb{R}$?

Jul 19, 2022

12

If $L^1$ average of $f$ is smaller than $t^2$ then $f=0$ a.e.

Aug 20, 2019

11

Compute $\prod^{100}_{n=1} \left(5-4 \cos \left(\frac{\pi (2n-1)}{100} \right) \right)$.

Aug 26, 2023

9

$a_n>0$, $\sum a_n^2<+\infty$, and $\sum a_{n_k}=+\infty$ whenever $\lim\limits_{k\to\infty}\frac{n_{k+1}}{n_k}=1\;?$

Dec 25, 2023

Questions

View all 48 questions

19

Let $ f(x)=\frac{1+\cos(2\pi x)}2$ and $f^n=f\circ f^{n-1}$. Is it true that for almost every $x$, $\lim_{n \to \infty} f^n(x)=1$?

Oct 23, 2022

14

Given a sequence with $a_1=1$ and $a_{n+1}=a_n-\frac13a_n^2$. Is there an easier way to get an upper bound of $1/a_{100}$?

Jun 19, 2022

10

Prove $\liminf_{n\to\infty} \left(n^2(4a_n(1-a_{n-1})-1)\right)\leq\frac14$ for any non-negative seqence $\{a_n\}$.

Jul 22, 2022

10

A random series has infinitely many zeros in $[0,1)$ almost surely.

May 11, 2019

8

If the Fourier coefficient $\hat{f}(k)$ of $f\in C^1(\mathbb T)$ is zero for all $|k|<N$, then $\|f\|_{L^\infty}\leq \frac CN \|f'\|_{L^\infty}$

Mar 7, 2023

Tags

View all 205 tags

real-analysis

370

Score

152

posts

calculus

157

Score

57

posts

integration

121

Score

34

posts

algebra-precalculus

111

Score

21

posts

sequences-and-series

106

Score

39

posts

Reputation

This user has no recent positive reputation changes.

Badges

View all badges

27

gold badges

Marshal

Dec 11, 2022
Electorate

Nov 20, 2022
Steward

× 24

Jan 4, 2024

26

silver badges

Refiner

Jul 30, 2022
Generalist

Dec 2, 2023
Deputy

Aug 24, 2019

46

bronze badges

algebra-precalculus

Dec 24, 2023
sequences-and-series

Dec 26, 2023
integration

Nov 27, 2022

Accounts

View all 7 accounts

14k
27
26
46

699
5
14

Meta Stack Exchange

101
2

101
3

Mathematics Educators

101
1

Active bounties (0)

This user has no active bounties

Votes cast

1,271

upvotes

27

downvotes

808

question votes

490

answer votes