# 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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### How can an imaginary equation give a real answer?

I came across this equation, $$e^{ix} = \cos(x) + i\sin(x)$$ This is the simplified version, the real one is more complex but this part is the one I have a question about. The right side clearly has ...
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### Help with interesting sum involving Euler's constant

Wikipedia gives an interesting infinite sum for Euler's constant $\gamma$ and I was wondering how one would evaluate this interesting sum. The sum is given as follows: Let $N_0 (x)$ and $N_1 (x)$ ...
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### Different Type of Euler's Circuit and Path (Different Looking Graph)

So I have become familiar with the basic graphs that have dots, and lines connection dot to dot. I know that a Euler's circuit is touching every edge of a graph once, and returning to the same point, ...
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### How to simplify this representation of $\gamma$?

I have a function of two variables, $Z(n,m) = (-1)^m \left( \frac{1}{m-2^n} + \frac{1}{2^n \log (2^n /m)} \right)$, and the infinite sum $\sum_{n=1}^{\infty} \sum_{m=1}^{2^n -1} Z(n,m) = \gamma$, the ...
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### Transform cos to e function

What are the steps in order to transform the cosine function to the exponential function: $$\left[\cos \left(\frac{k \pi} N\right)\right]^n \approx e ^ {\frac{-n}2 \left(\frac{k \pi} N \right)^2}$$...
### Evaluating $\int{e^{-t^{2}}\,dt}$
Let $f(x) = e^{x}$, which, expressed as a Maclaurin series, is equal to: $$\sum_{i = 0}^{\infty}{\frac{x^{i}}{i!}}$$ Therefore, $f(-t^{2})$ gives: \sum_{i = 0}^{\infty}{\frac{(-t^{2})^{i}}{i!}} = ...