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Darío A. Gutiérrez


My favorite Zitate

-"Sir, an equation has no meaning for me unless it expresses a thought of God." (Srinivasa Ramanujan)

-"Denn die Mathematik ist es, die uns vor dem Trug der Sinne schützt und die uns den Unterschied zwischen Schein und Wahrheit kennen lehrt.." (Leonhard Euler)


My favorite Identity
\begin{align} e &= 2,71828182845904523… \\ \pi &= 3,14159265358979323… \\ i&=\sqrt{-1}\\\\ \end{align}

\begin{align} e^{i\pi} &= 1 + i\pi + \frac{(i\pi)^2}{2!} + \frac{(i\pi)^3}{3!} + \frac{(i\pi)^4}{4!} + \frac{(i\pi)^5}{5!} + \cdots \\ &= 1 + i\pi - \frac{\pi^2}{2!} - \frac{i\pi^3}{3!} + \frac{\pi^4}{4!} + \frac{i\pi^5}{5!} - \cdots \\ &= \left( 1 - \frac{\pi^2}{2!} + \frac{\pi^4}{4!} - \cdots \right) + i\left( \pi - \frac{\pi^3}{3!} + \frac{\pi^5}{5!} - \cdots \right) \\ &= \cos(\pi) + i\sin(\pi) \\ &= -1 \end{align}

$$e^{i\pi} = -1$$ enter image description here




My favorite Answers on Mathematics StackExchange:

How can I calculate $\alpha=\arccos\left(-\frac{1}{4}\right)$ without using a calculator?

Compute : $\int\frac{x+2}{\sqrt{x^2+5x}+6}~dx$

Prove that $\sum_{k=0}^nk{m+k \choose m}=n{m+n+1\choose m+1}-{m+n+1 \choose m+2}$

Why is $\Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}$ ?


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