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cheat-sheets/analysis/Analysis_Wichtige_Formeln.tex
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@ -45,10 +45,10 @@
\centering
\begin{align*}
\cosh x = \frac {1}{2} (e^x + e^{-x}) &= \scriptstyle \sum_{n = 0}^{\infty} \frac {x^{2n}}{(2n)!} \\
\cosh x = \frac {1}{2} (e^x + e^{-x}) &= \sum_{n = 0}^{\infty} \frac {x^{2n}}{(2n)!} \\
\sinh x = \frac {1}{2} (e^x - e^{-x}) &= \sum_{n = 0}^{\infty} \frac {x^{2n + 1}}{(2n + 1)!} \\
e^x &= \sum_{n = 0}^{\infty} \frac {x^n}{n!} \\
\sum_{n = 0}^{\infty} (-1)^n \frac {x^{n + 1}}{n + 1} &= \log (1+x) (x \in (-1,1)) \\
e^x &= \sum_{n = 0}^{\infty} \frac {x^n}{n!} = \lim_{n\to\infty} \left (1+\frac{x}{n} \right )^n\\
\sum_{n = 0}^{\infty} (-1)^n \frac {x^{n + 1}}{n + 1} &= \log (1+x) \; x \in (-1,1) \\
\sum_{n = 0}^{\infty} x^n &= \frac {1}{1 - x} (x \in (-1,1)) \\
0,\bar{3} &= \sum_{n = 1}^{\infty} \frac {3}{(10)^n}
\end{align*}