Summary

Reputation

25,810

25.8k
20.2k
14.6k

2021
2022
2023
2024

Next tag badge

harmonic-numbers

986/1000 score

327/200 answers

Badges

119

Newest

Nice Question

Next badge

50/80

Strunk & White

Impact

~280k

people reached

posts edited

helpful flag

376

votes cast

Answers

View all 498 answers

Compute $\sum_{n=1}^\infty\frac{H_n^2H_n^{(2)}}{n^3}$

Aug 5, 2019

Prove $\zeta(3)=2\sum_{n=1}^\infty\frac{H_n}{n}\left[\frac1{4^n}{2n\choose n}\left(H_{2n}-H_n-\frac1{2n}-\ln2\right)+\frac1{2n}\right]$

Nov 7, 2019

How can I prove $\frac{\gamma}{2}=\int_{0}^{\infty}\frac{e^{-x^{2}}-e^{-x}}{x}\text{d}x$?

Aug 2, 2019

How to compute $\sum_{n=1}^\infty\frac{(-1)^nH_n}{n^4}$ by real integration only?

Nov 25, 2019

Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$

Apr 27, 2019

Questions

View all 163 questions

Are these generalizations known in the literature?

Mar 6, 2022

Challenging problem: Calculate $\int_0^{2\pi}x^2 \cos(x)\operatorname{Li}_2(\cos(x))dx$

Oct 7, 2020

Prove $ \int_0^1 \frac{\ln^a(1-x)\ln(1+x)}{x}dx=(-1)^a a! \sum_{n=1}^\infty\frac{H_n^{(a+1)}}{n2^n}$

Jul 14, 2019

Compute $\sum_{n=1}^\infty\frac{H_n^2H_n^{(2)}}{n^3}$

Aug 5, 2019

Challenging integral: Evaluate $\int_0^1\frac{\ln^3(1-x)\operatorname{Li}_3(x)}{x}dx$

Aug 7, 2019

Reputation

+10

How to evaluate the sum $\sum_{n=1}^{\infty}\frac{1}{(2n+1)(2n+2)}\left(1+\frac{1}{2}+...+\frac{1}{n}\right)$

+10

Prove $ \int_0^1 \frac{\ln^a(1-x)\ln(1+x)}{x}dx=(-1)^a a! \sum_{n=1}^\infty\frac{H_n^{(a+1)}}{n2^n}$

+10

Are these generalizations known in the literature?

+10

Is there any closed form for $\frac{d^{2 n}( \cot z)}{d z^{2 n}}\big|_{z=\frac{\pi}{4}}$?

Badges

View all badges

gold badges

integration

Feb 3
Socratic

Aug 17, 2020
Fanatic

Jul 25, 2019

silver badges

harmonic-numbers

Dec 6, 2019
definite-integrals

Sep 17, 2021
sequences-and-series

Jun 12, 2020

119

bronze badges

polylogarithm

Aug 27, 2019
closed-form

Aug 9, 2019
improper-integrals

Oct 23

Accounts

Mathematics

25.8k
3
56
119

Academia

Mathematica

TeX - LaTeX

MathOverflow

Active bounties (0)

This user has no active bounties

Votes cast

375

upvotes

downvotes

106

question votes

270

answer votes

User feed

Stack Exchange Network

Summary

Reputation

25,810

Badges

Newest

Next badge

Impact

Answers

Questions

Tags

Reputation

Badges

Accounts

Active bounties (0)

Votes cast