# Tagged Questions

For questions related to Euler's constant $\gamma$, which is defined to be the limiting difference between the natural logarithm and the harmonic series.

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### Derivative of Riemann zeta, is this inequality true?

Is the following inequality true? $$\gamma -\frac{\zeta ''(-2\;n)}{2 \zeta '(-2\;n)} > \log (n)-\gamma$$ This for $n$ a positive integer, $n=1,2,3,4,5,...$, and more precisely when $n$ approaches ...
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### Is this Euler-Mascheroni constant calculation from double integrals a true identity?

A prime number is a number that is only divisible by itself and one, that is the number of divisors of a prime number is equal to $2$. One way to illustrate this is to plot a matrix such that if the ...
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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 $1$ [duplicate]

Need some help here. I need prove that the following limit exist and is less than $1$ $$\lim_{x\to\infty}\left(\sum_{n\le x}^{}\frac{1}{n}-\ln x\right)$$ I feel a little lost here, this is my first ...
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### Integral representation of Euler's constant

Prove that : $$\gamma=-\int_0^{1}\ln \ln \left ( \frac{1}{x} \right) \ \mathrm{d}x.$$ where $\gamma$ is Euler's constant ($\gamma \approx 0.57721$). This integral was mentioned in Wikipedia as in ...
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### “How I wish I could calculate pi” analogs…

You might know the mnemonic for $\pi$ in the title or even this more elaborated one: Sir, I bear a rhyme excelling In mystic force, and magic spelling Celestial sprites elucidate All my own ...