List questions from euler-mascheroni-constant

Published on 01 Jul 2016 - 18:42

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Reference for proof of harmonic number asymptotic expansion

Published on 06 Apr 2013 - 5:05

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Need to show that $\lim_{x\to\infty}\left(\sum_{n\le x}^{}\frac{1}{n}-\ln x \right)$ exist and is less than $1$

Published on 05 Jun 2013 - 21:13

793

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Is this Euler-Mascheroni constant calculation from double integrals a true identity?

Published on 09 Jun 2013 - 13:58

499

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Why does $\gamma=\lim_{s\to1^+}\sum_{n=1}^{\infty}\left(\frac{1}{n^s}-\frac{1}{s^n}\right)=\lim_{s\to0}\frac{\zeta(1+s)+\zeta(1-s)}{2}$?

Published on 15 Jul 2013 - 12:27

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Continued fraction of $\gamma+1$ using recursion

Published on 09 Aug 2013 - 20:41

138

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Proving this identity $\gamma=1+\ln(\frac{1}{2})+\sum_{k=1}^{\infty}(-1)^{k+1}\frac{\zeta(k+1)-1}{k+1}$ where $\gamma$ is the Euler-Masceroni constant

Published on 14 Aug 2013 - 11:33

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Why is $-\gamma = \int_0^1 \frac{e^{-z}-1}{z}dz+\int_1^\infty \frac{e^{-z}}{z}dz$

Published on 06 Sep 2013 - 9:50

836

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Infinite Series $\sum\limits_{n=1}^{\infty}\frac{(-1)^n}{n}\left\lfloor\frac{\log(n)}{\log(2)}\right\rfloor$

Published on 30 Sep 2013 - 11:51

172

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Integral $\int_0^{\infty} \log(x) e^{-x^2} \mathrm{d}x = -\frac{1}{4}\sqrt{\pi} (\gamma + \log(4)).$

Published on 27 Nov 2013 - 7:50

403

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Question on Macys formula for Euler-Mascheroni Constant $\gamma$

Published on 13 Dec 2013 - 11:02

25.8k

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Simple proof Euler–Mascheroni $\gamma$ constant

Published on 06 Jan 2014 - 23:55

2.9k

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What is the limit of difference between harmonic series and natural logarithm of n+1?

Published on 16 Jan 2014 - 22:35

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An Euler-Mascheroni-like sequence

Published on 28 Jan 2014 - 15:00

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Intuitively, why is the Euler-Mascheroni constant near $\sqrt{1/3}$?

Published on 29 Jan 2014 - 18:12

List Question

Natural log operation on $e^{i \tau}$

Reference for proof of harmonic number asymptotic expansion

Need to show that $\lim_{x\to\infty}\left(\sum_{n\le x}^{}\frac{1}{n}-\ln x \right)$ exist and is less than $1$

Is this Euler-Mascheroni constant calculation from double integrals a true identity?

Why does $\gamma=\lim_{s\to1^+}\sum_{n=1}^{\infty}\left(\frac{1}{n^s}-\frac{1}{s^n}\right)=\lim_{s\to0}\frac{\zeta(1+s)+\zeta(1-s)}{2}$?

Continued fraction of $\gamma+1$ using recursion

Proving this identity $\gamma=1+\ln(\frac{1}{2})+\sum_{k=1}^{\infty}(-1)^{k+1}\frac{\zeta(k+1)-1}{k+1}$ where $\gamma$ is the Euler-Masceroni constant

Why is $-\gamma = \int_0^1 \frac{e^{-z}-1}{z}dz+\int_1^\infty \frac{e^{-z}}{z}dz$

Infinite Series $\sum\limits_{n=1}^{\infty}\frac{(-1)^n}{n}\left\lfloor\frac{\log(n)}{\log(2)}\right\rfloor$

Integral $\int_0^{\infty} \log(x) e^{-x^2} \mathrm{d}x = -\frac{1}{4}\sqrt{\pi} (\gamma + \log(4)).$

Question on Macys formula for Euler-Mascheroni Constant $\gamma$

Simple proof Euler–Mascheroni $\gamma$ constant

What is the limit of difference between harmonic series and natural logarithm of n+1?

An Euler-Mascheroni-like sequence

Intuitively, why is the Euler-Mascheroni constant near $\sqrt{1/3}$?

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