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### How do you calculate the decimal expansion of an irrational number?

Just curious, how do you calculate an irrational number? Take $\pi$ for example. Computers have calculated $\pi$ to the millionth digit and beyond. What formula/method do they use to figure this out? ...
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### Intuitively, why is the Euler-Mascheroni constant near $\sqrt{1/3}$?

Questions that ask for "intuitive" reasons are admittedly subjective, but I suspect some people will find this interesting. Some time ago, I was struck by the coincidence that the Euler-Mascheroni ...
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### Evaluation of Euler's Constant $\gamma$

Long back I had seen (in some obscure book) a formula to calculate the value of Euler's constant $\gamma$ based on a table of values of Riemann zeta function $\zeta(s)$. I am not able to recall the ...
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### Euler-Mascheroni constant expression, further simplification

The Euler-Mascheroni constant gamma is defined as: $$\gamma=\lim\limits_{n \rightarrow \infty}\left(\sum\limits_{m=1}^{n} \frac{1}{m} - \log(n)\right)$$ From this previous question Do these series ...
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### $\lim_{n\to\infty} f(2^n)$ for some very slowly increasing function $f(n)$

I should be able to answer this myself, but feel insecure anyway. I want to know, whether a function f(n) is bounded if n goes to infinity (and if it's bounded, the limit). Heuristically it appears (...
I was reading some articles on the digamma function, and I was wondering if anyone knows how to express the digamma function $\psi^{(0)}(n)$ in terms of a trigonometric function or a logarithmic ...