Question

Euler-Mascheroni constant: understanding why $\lim_{m\rightarrow \infty} \sum_{n=1}^{m} (\ln (1 + \frac{1}{n})-\frac{1}{n+1})= 1 - \gamma$

score 880 · Answer 1 · 2014-02-02 15:04:13

880

Views

Euler-Mascheroni constant: understanding why $\lim_{m\rightarrow \infty} \sum_{n=1}^{m} (\ln (1 + \frac{1}{n})-\frac{1}{n+1})= 1 - \gamma$

Published on 02 Feb 2014 - 15:04

score 172 · Answer 2 · 2026-03-26 05:46:07

172

Views

About Abel Summation

Published on 26 Mar 2026 - 5:46

score 234 · Answer 3 · 2017-04-10 05:14:12

234

Views

How do we prove this conjecture $\int_{0}^{\infty}e^{-\sqrt{x}}\ln{\left(1+{1\over \sqrt{x}}\right)}=2\gamma ?$

Published on 10 Apr 2017 - 5:14

score 344 · Answer 4 · 2017-04-20 14:40:33

344

Views

How to show $\int_{0}^{\infty}{{\gamma+\ln x\over e^x}}\cdot{1-\cos x\over x} \,\mathrm dx={1\over 2}\cdot{\pi-\ln 4\over 4}\cdot{\pi+\ln4\over 4}?$

Published on 20 Apr 2017 - 14:40

score 834 · Answer 5 · 2017-04-21 21:36:29

834

Views

How can I get $1-2e^{-jw} + e^{-2jw}=(1-e^{-jw})^2$?

Published on 21 Apr 2017 - 21:36

score 378 · Answer 6 · 2026-03-25 16:06:20

378

Views

Using Euler's relation to transform to cosine

Published on 25 Mar 2026 - 16:06

score 338 · Answer 7 · 2017-04-26 19:19:43

338

Views

Error of approximation for Euler's constant

Published on 26 Apr 2017 - 19:19

score 101 · Answer 8 · 2017-05-03 09:14:34

101

Views

Why does e pop up as the average of "dice rolls" of [0...x[ needed to reach/exceed x?

Published on 03 May 2017 - 9:14

score 263 · Answer 9 · 2017-05-08 12:04:43

263

Views

How to show that $\gamma=\lim\limits_{n \to \infty}\left(\sum\limits_{k=1}^{n}{\zeta(2k)\over k}\right)-\ln(2n)$

Published on 08 May 2017 - 12:04

score 495 · Answer 10 · 2017-05-11 04:30:40

495

Views

Prove that $\lim\limits_{k\to\infty}\left(\frac1k\sum\limits_{n=1}^k\left\lfloor\frac kn\right\rfloor-\ln k\right)=2\gamma-1$

Published on 11 May 2017 - 4:30

score 113 · Answer 11 · 2017-05-12 11:43:13

113

Views

How may one show that $\int_{0}^{\infty}x^{n-1}e^{-x^n}\ln^2(x)\mathrm dx={6\gamma^2+\pi^2\over 6n^3}?$

Published on 12 May 2017 - 11:43

score 70 · Answer 12 · 2026-03-25 18:28:45

70

Views

Solving for a variable that's an index of e

Published on 25 Mar 2026 - 18:28

score 162 · Answer 13 · 2017-05-20 10:14:34

162

Views

Can we determine approximate value of $\sum\limits_{n=0}^{k}\frac{1}{an+b}$?

Published on 20 May 2017 - 10:14

score 108 · Answer 14 · 2017-05-24 09:14:10

108

Views

Calculating the remainder of the series $1/n!$ (euler number)

Published on 24 May 2017 - 9:14

score 248 · Answer 15 · 2017-06-01 06:01:42

248

Views

A generalization of the Euler-Mascheroni constant

Published on 01 Jun 2017 - 6:01

List Question

Euler-Mascheroni constant: understanding why $\lim_{m\rightarrow \infty} \sum_{n=1}^{m} (\ln (1 + \frac{1}{n})-\frac{1}{n+1})= 1 - \gamma$

About Abel Summation

How do we prove this conjecture $\int_{0}^{\infty}e^{-\sqrt{x}}\ln{\left(1+{1\over \sqrt{x}}\right)}=2\gamma ?$

How to show $\int_{0}^{\infty}{{\gamma+\ln x\over e^x}}\cdot{1-\cos x\over x} \,\mathrm dx={1\over 2}\cdot{\pi-\ln 4\over 4}\cdot{\pi+\ln4\over 4}?$

How can I get $1-2e^{-jw} + e^{-2jw}=(1-e^{-jw})^2$?

Using Euler's relation to transform to cosine

Error of approximation for Euler's constant

Why does e pop up as the average of "dice rolls" of [0...x[ needed to reach/exceed x?

How to show that $\gamma=\lim\limits_{n \to \infty}\left(\sum\limits_{k=1}^{n}{\zeta(2k)\over k}\right)-\ln(2n)$

Prove that $\lim\limits_{k\to\infty}\left(\frac1k\sum\limits_{n=1}^k\left\lfloor\frac kn\right\rfloor-\ln k\right)=2\gamma-1$

How may one show that $\int_{0}^{\infty}x^{n-1}e^{-x^n}\ln^2(x)\mathrm dx={6\gamma^2+\pi^2\over 6n^3}?$

Solving for a variable that's an index of e

Can we determine approximate value of $\sum\limits_{n=0}^{k}\frac{1}{an+b}$?

Calculating the remainder of the series $1/n!$ (euler number)

A generalization of the Euler-Mascheroni constant

Trending Questions

Popular # Hahtags

Popular Questions