Mathematische Formeln in Dokuwiki

In modernen Wikis (mit installiertem Math-Plugin) kann die Latex-Syntax für Formeln eingesetzt werden. Die Befehle sind überraschend einfach und das Ergebnis überzeugend!

Bitte unbedingt von oben nach unten lesen. Es ist für alle etwas dabei: Einsteiger eher weiter oben suchen, nach unten eher für Fortgeschrittene!

Mit der folgenden Syntax erkennt das installierte Plugin den Code für mathematische Befehle, der dann kompiliert wird:

Dieses ist eine wichtige Formel: $c = a + b$

Dieses ist eine wichtige Formel: $c = a + b$

Für alle Zahlen $a_1, \dots, a_n$ gilt

Für alle Zahlen $a_1, \dots, a_n$ gilt

Seien $a$ und $b$ die Katheten und $c$ die Hypotenuse, dann gilt
$c=\sqrt{a^2+b^2}$ (Lehrsatz des Pythagoras).

Seien $a$ und $b$ die Katheten und $c$ die Hypotenuse, dann gilt $c=\sqrt{a^2+b^2}$ (Lehrsatz des Pythagoras).

Dieses ist eine wichtige Formel: $$y = f(x) = k~x + d$$

Dieses ist eine wichtige Formel: $$y = f(x) = k~x + d$$

Seien $a$ und $b$ die Katheten und $c$ die Hypotenuse, dann gilt $$c^2=a^2+b^2$$
(Lehrsatz des Pythagoras).

Seien $a$ und $b$ die Katheten und $c$ die Hypotenuse, dann gilt $$c^2=a^2+b^2$$ (Lehrsatz des Pythagoras).

$ab$, $a\,b$, $a\:b$, $a\;b$, $a\!b$, $a \quad b$, $a \qquad b$

$ab$, $a\,b$, $a\:b$, $a\;b$, $a\!b$, $a \quad b$, $a \qquad b$

\begin{eqnarray}
f(x) & = & \cos x \\
f’(x) & = & - \sin x \\
\int_0^xf(y)\mathrm{d}y&=&\sin x
\end{eqnarray}

$$\begin{eqnarray} f(x) & = & \cos x \\ f’(x) & = & - \sin x \\ \int_0^xf(y)\mathrm{d}y&=&\sin x \end{eqnarray}$$ Das Zeichen & dient zur Ausrichtung der Zeilen, \\ erzeugt eine neue Zeile

\begin{eqnarray}\label{eq:4}
 & a+b & c+d\\
 & x+y & u+v\\
\end{eqnarray}

$$\begin{eqnarray} & a+b & c+d\\ & x+y & u+v \end{eqnarray}$$

\begin{eqnarray*}
 & a+b & c+d\\
 & x+y & u+v\\
\end{eqnarray*}

$$\begin{eqnarray*} & a+b & c+d\\ & x+y & u+v \end{eqnarray*}$$

$ \mathrm{A}\mathrm{B}\Gamma\Delta\mathrm{E}\mathrm{Z}\mathrm{H}\Theta\mathrm{I}\mathrm{K}\Lambda
\mathrm{M}\mathrm{N}\Xi\mathrm{O}\Pi\mathrm{P}\Sigma\mathrm{T}\Phi\mathrm{X}\mathrm{Y}\Psi\Omega$

$\mathrm{A}\mathrm{B}\Gamma\Delta\mathrm{E}\mathrm{Z}\mathrm{H}\Theta\mathrm{I}\mathrm{K}\Lambda \mathrm{M}\mathrm{N}\Xi\mathrm{O}\Pi\mathrm{P}\Sigma\mathrm{T}\Phi\mathrm{X}\mathrm{Y}\Psi\Omega$

$ \alpha\beta\gamma\delta\epsilon\zeta\eta\theta\iota\kappa\lambda\mu\nu\xi\mathrm{o}\pi\rho\sigma\tau\phi\chi\upsilon\psi\omega$

$\alpha\beta\gamma\delta\epsilon\zeta\eta\theta\iota\kappa\lambda\mu\nu\xi\mathrm{o}\pi\rho\sigma\tau\phi\chi\upsilon\psi\omega$

$\varepsilon \quad \vartheta \quad \varpi \quad \varrho \quad \varsigma \quad \varphi$

$\varepsilon \quad \vartheta \quad \varpi \quad \varrho \quad \varsigma \quad \varphi$

$\aleph\quad\Re\quad\Im\quad\partial\quad\infty\quad\forall\quad\exists\quad\neg\quad\in\quad\heartsuit$

$\aleph\quad\Re\quad\Im\quad\partial\quad\infty\quad\forall\quad\exists\quad\neg\quad\in\quad\heartsuit$

$ \forall \varepsilon>0:|f(x_1)-f(x_2)| < \varepsilon\quad\exists\eta: |x_1-x_2|<\eta$

$\forall \varepsilon>0:|f(x_1)-f(x_2)| < \varepsilon\quad\exists\eta: |x_1-x_2|<\eta$

Eurozeichen mit Unicode: $ \unicode{0x20AC}$

Eurozeichen mit Unicode: $\unicode{0x20AC}$

$ ( ~ \lbrack ~ \lbrace ~ [ ~ \lfloor ~ \langle ~ \{ ~ \lceil$

$( ~ \lbrack ~ \lbrace ~ [ ~ \lfloor ~ \langle ~ \{ ~ \lceil$

$ ) ~ \rbrack ~ \rbrace ~ ]~ \rfloor ~ \rangle ~ \} ~  \rceil$

$) ~ \rbrack ~ \rbrace ~ ]~ \rfloor ~ \rangle ~ \} ~ \rceil$

$ \Bigl( (x+1) (x-1)\Bigr) ^2$

$\Bigl( (x+1) (x-1)\Bigr) ^2$

$ \left( (x+1) (x-1)\right) ^2$

$\left( (x+1) (x-1)\right) ^2$

$ 1 + \left(\frac{1}{1-x^2}\right)$

$1 + \left(\frac{1}{1-x^2}\right)$

$ \underbrace{\overbrace{a + b + \cdots +z}^{26} + \overbrace{A + B + \cdots+Z}^{26}}_{52}$

$\underbrace{\overbrace{a + b + \cdots +z}^{26} + \overbrace{A + B + \cdots+Z}^{26}}_{52}$

$ \overline{m+n} \qquad \underline{m+n}$

$\overline{m+n} \qquad \underline{m+n}$

$x = y > z \qquad x := y \qquad x \le y \ne z $

$x = y > z \qquad x := y \qquad x \le y \ne z$ $x \sim y \simeq z \qquad x \equiv y \not\equiv z \qquad x \subset y \subseteq z$ $x \sim y \simeq z \qquad x \equiv y \not\equiv z \qquad x \subset y \subseteq z$

$x + y - z \qquad x * y / z \qquad x \times y \cdot z$

$x + y - z \qquad x * y / z \qquad x \times y \cdot z$

$x \circ y \bullet z \qquad x \cup y \cap z \qquad x \sqcup y \sqcap z$

$x \circ y \bullet z \qquad x \cup y \cap z \qquad x \sqcup y \sqcap z$

$x \vee y \wedge z\qquad x \pm y \mp z$

$x \vee y \wedge z\qquad x \pm y \mp z$

$ \hat a \qquad \check b \qquad \tilde c \qquad \acute d \qquad \grave e$

$\hat a \qquad \check b \qquad \tilde c \qquad \acute d \qquad \grave e$

$ \dot f\qquad\ddot g\qquad\breve h \qquad \bar k \qquad \vec l$

$\dot f\qquad\ddot g\qquad\breve h \qquad \bar k \qquad \vec l$

$ \hat\imath \qquad \check\jmath$

$\hat\imath \qquad \check\jmath$

$ \widehat x \qquad \widehat{xy} \qquad \widehat{xyz}$

$\widehat x \qquad \widehat{xy} \qquad \widehat{xyz}$

$ \widetilde x \qquad \widetilde{xy} \qquad \widetilde{xyz}$

$\widetilde x \qquad \widetilde{xy} \qquad \widetilde{xyz}$

$ \alpha \cdot(\vec x + \vec y) = \alpha \cdot \vec x + \alpha \cdot \vec y$

$\alpha \cdot(\vec x + \vec y) = \alpha \cdot \vec x + \alpha \cdot \vec y$

$ \vec x \cdot (\vec y \cdot \vec z) \not=(\vec x\cdot\vec y)\cdot \vec z$

$\vec x \cdot (\vec y \cdot \vec z) \not=(\vec x\cdot\vec y)\cdot \vec z$

$ \vec x\times (\vec y\times \vec z) \not= (\vec x \times \vec y) \times \vec z$

$\vec x\times (\vec y\times \vec z) \not= (\vec x \times \vec y) \times \vec z$

$ \leftarrow \qquad \Leftarrow \qquad \leftrightarrow \qquad
\Leftrightarrow \qquad \uparrow\qquad\downarrow\qquad\nearrow$

$\leftarrow \qquad \Leftarrow \qquad \leftrightarrow \qquad \Leftrightarrow \qquad \uparrow\qquad\downarrow\qquad\nearrow$

$\longleftarrow\qquad\leftharpoonup \qquad \mapsto \qquad \leadsto$

$\longleftarrow\qquad\leftharpoonup \qquad \mapsto \qquad \leadsto$

$ (\mathcal{A} \Rightarrow \mathcal{B}) \Longleftrightarrow
(\lnot \mathcal{B} \Rightarrow \lnot \mathcal{A})$

$(\mathcal{A} \Rightarrow \mathcal{B}) \Longleftrightarrow (\lnot \mathcal{B} \Rightarrow \lnot \mathcal{A})$

$(\mathcal{A} \Longleftrightarrow \mathcal{B}) \Longleftrightarrow
(\mathcal{A}\Rightarrow \mathcal{B}) \wedge (\mathcal{B}\Rightarrow\mathcal{A})$

$(\mathcal{A} \Longleftrightarrow \mathcal{B}) \Longleftrightarrow (\mathcal{A}\Rightarrow \mathcal{B}) \wedge (\mathcal{B}\Rightarrow\mathcal{A})$

$ \forall x\in\mathbf{R}: x^2\ge0$

$\forall x\in\mathbf{R}: x^2\ge0$

\begin{eqnarray*}
\mathbf{A} \cdot \mathbf{x} & = &
\mathbf{y} \\
\textrm{mit } \mathbf{A}&=&(a_{ij})\\
&&i=1,\cdots, m; j=1,\cdots, n\\
\mathbf{x} & = & (x_1,\cdots, x_n)
\textrm{ und}\\
\mathbf{y} & = & (y_1, \cdots, y_m)\\
\end{eqnarray*}

$$\begin{eqnarray*} \mathbf{A} \cdot \mathbf{x} & = & \mathbf{y} \\ \textrm{mit } \mathbf{A}&=&(a_{ij})\\ &&i=1,\cdots, m; j=1,\cdots, n\\ \mathbf{x} & = & (x_1,\cdots, x_n) \textrm{ und}\\ \mathbf{y} & = & (y_1, \cdots, y_m)\\ \end{eqnarray*}$$

$ \displaystyle a_i \qquad a_{\displaystyle i_j} $

$\displaystyle a_i \qquad a_{\displaystyle i_j}$

$ \displaystyle a^{\displaystyle i} \qquad a^{\displaystyle i^j} $

$\displaystyle a^{\displaystyle i} \qquad a^{\displaystyle i^j}$

$ _1x_2 \qquad x^3_4 \qquad a^{b^\alpha_\beta}_{c^\gamma_\delta} \qquad F^1_2 \qquad F{}^1_2$

$_1x_2 \qquad x^3_4 \qquad a^{b^\alpha_\beta}_{c^\gamma_\delta} \qquad F^1_2 \qquad F{}^1_2$

$ \displaystyle _1x_2 = \sqrt{\left(\frac{p}{2}\right)^2-q}$

$\displaystyle _{ \displaystyle 1}x_2 = -\frac{p}{2}\pm \sqrt{\left(\frac{p}{2}\right)^2-q}$

$ \displaystyle \frac{1}{2} \qquad \frac{n+1}{3}$

$\displaystyle \frac{1}{2} \qquad \frac{n+1}{3}$

$ \displaystyle \frac{x+y^2}{m+1} \qquad \frac{x+y^2}{m} + 1 \qquad x + \frac{y^2}{m}+1$

$\displaystyle \frac{x+y^2}{m+1} \qquad \frac{x+y^2}{m} + 1 \qquad x + \frac{y^2}{m}+1$

$x + \frac{\displaystyle y^2}{\displaystyle m+1} \qquad x + y^\frac{\displaystyle 2}{\displaystyle m+1}$

$x + \frac{\displaystyle y^2}{\displaystyle m+1} \qquad x + y^\frac{\displaystyle 2}{\displaystyle m+1}$

$ \displaystyle x + \frac{y^2}{m+1} \qquad x + y^\frac{2}{m+1}$

$\displaystyle x + \frac{y^2}{m+1} \qquad x + y^\frac{2}{m+1}$

$ \displaystyle \frac{\frac{x}{y}}{2} \qquad \frac{x}{\frac{y}{2}}$

$\displaystyle \frac{\frac{x}{y}}{2} \qquad \frac{x}{\frac{y}{2}}$

$x_0 + \frac{1}{x_1 + 
\frac{1}{x_2 +
\frac{1}{x_3 +
\frac{1}{x_4}}}}$

$x_0 + \frac{1}{x_1 + \frac{1}{x_2 + \frac{1}{x_3 + \frac{1}{x_4}}}}$

$ \displaystyle x_0 + \frac{1}{\displaystyle x_1 +
\frac{\strut 1}{\displaystyle x_2 +
\frac{\strut 1}{\displaystyle x_3 + 
\frac{\strut 1}{\displaystyle x_4}}}}$

$\displaystyle x_0+\frac{1}{\displaystyle x_1 + \frac{\strut 1}{\displaystyle x_2 + \frac{\strut 1}{\displaystyle x_3 + \frac{\strut 1}{\displaystyle x_4}}}}$

$ \sqrt 2 \qquad \sqrt{\displaystyle x^2-y^2} \qquad \sqrt{\alpha^2 + \beta^2 - \gamma^2}$

$\sqrt 2 \qquad \sqrt{\displaystyle x^2-y^2} \qquad \sqrt{\alpha^2 + \beta^2 - \gamma^2}$

$ \sqrt[3]{2} \qquad \sqrt[n]{\sqrt\alpha + \sqrt\beta} \qquad \sqrt[n+1]{a^n + b^n}$

$\sqrt[3]{2} \qquad \sqrt[n]{\sqrt\alpha + \sqrt\beta} \qquad \sqrt[n+1]{a^n + b^n}$

$ \sqrt a +\sqrt{b^2} +\sqrt c \qquad \sqrt{\mathstrut a} + \sqrt{\mathstrut b^2} + \sqrt{\mathstrut c}$

$\sqrt a +\sqrt{b^2} +\sqrt c \qquad \sqrt{\mathstrut a} + \sqrt{\mathstrut b^2} + \sqrt{\mathstrut c}$

$ \sqrt{1+ \sqrt{1+ \sqrt{1+ \sqrt{1+ \sqrt{1 + \sqrt{1+x}}}}}}$

$\sqrt{1+ \sqrt{1+ \sqrt{1+ \sqrt{1+ \sqrt{1 + \sqrt{1+x}}}}}}$

${n \choose 2} \qquad {n+1 \choose k} \qquad \frac{\displaystyle{n \choose k}}{\displaystyle 2}$

${n \choose 2} \qquad {n+1 \choose k} \qquad \frac{\displaystyle{n \choose k}}{\displaystyle 2}$

${x \atop a+b} \qquad {n \atop k+1}$

${x \atop a+b} \qquad {n \atop k+1}$

$ \displaystyle \sum_{{\scriptstyle 1 \le i \le p \atop \scriptstyle 1 \le j \le q}} a_{ij} b_{ji}$

$\displaystyle \sum_{{\scriptstyle 1 \le i \le p \atop \scriptstyle 1 \le j \le q}} a_{ij} b_{ji}$

$ \displaystyle f\prime(x) = \lim_{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}$

$\displaystyle f\prime(x) = \lim_{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}$

\begin{eqnarray*}
f(x) & = & \cos x \\
f’(x) & = & -\sin x \\
f’’(x) & = & -\cos x \\
\end{eqnarray*}

$$\begin{eqnarray*} f(x) & = & \cos x \\ f’(x) & = & -\sin x \\ f’’(x) & = & -\cos x \\ \end{eqnarray*}$$

\begin{eqnarray*}
h(x) & = & f(x) \cdot g(x)\\
\frac{h(x)}{\mathrm{d}x} & = & f(x)\cdot\frac{g(x)}{\mathrm{d}x}+\frac{f(x)}{\mathrm{d}x} \cdot g(x)
\end{eqnarray*}

$$\begin{eqnarray*} h(x) & = & f(x) \cdot g(x)\\ \frac{h(x)}{\mathrm{d}x} & = & f(x)\cdot\frac{g(x)}{\mathrm{d}x}+\frac{f(x)}{\mathrm{d}x} \cdot g(x) \end{eqnarray*}$$

\begin{eqnarray*}
\mathbf{x} & = & \frac{1}{2} \mathbf{k} \cdot t^2 + \mathbf{v_0} \cdot t + \mathbf{x_0}\\
\dot \mathbf{x} & = & \mathbf{k} \cdot t + \mathbf{v_0}\\
\ddot \mathbf{x} & = & \mathbf{k}
\end{eqnarray*}

\begin{eqnarray*}
\mathbf{x} & = & \frac{1}{2} \mathbf{k} \cdot t^2 + \mathbf{v_0} \cdot t + x_0\\
\dot{\mathbf{x}} & = & \mathbf{k} \cdot t + \mathbf{v_0}\\
\ddot{\mathbf{x}} & = & \mathbf{k}
\end{eqnarray*}

$$\begin{eqnarray*} \mathbf{x} & = & \frac{1}{2} \mathbf{k} \cdot t^2 + \mathbf{v_0} \cdot t + x_0\\ \dot{\mathbf{x}} & = & \mathbf{k} \cdot t + \mathbf{v_0}\\ \ddot{\mathbf{x}} & = & \mathbf{k} \end{eqnarray*}$$

\begin{eqnarray*}
z (x, y) & = & xy\\
\frac{\partial z}{\partial x} & = & y \quad \textrm{und}\\
\frac{\partial z}{\partial y} & = & x
\end{eqnarray*}

$$\begin{eqnarray*} z (x, y) & = & xy\\ \frac{\partial z}{\partial x} & = & y \quad \textrm{und}\\ \frac{\partial z}{\partial y} & = & x \end{eqnarray*}$$

\begin{eqnarray*}
z (x, y) & = & \frac{xy}{x^2+y^2} \quad(\forall x,y:x^2+y^2\not=0)\\
\frac{\partial z}{\partial x} & = & \frac{y(y^2-x^2)}{(x^2+y^2)^2} \qquad \textrm{und}\\
\frac{\partial z}{\partial y} & = & \frac{x(x^2-y^2)}{(x^2+y^2)^2}
\end{eqnarray*}

$$\begin{eqnarray*} z (x, y) & = & \frac{xy}{x^2+y^2} \quad(\forall x,y:x^2+y^2\not=0)\\ \frac{\partial z}{\partial x} & = & \frac{y(y^2-x^2)}{(x^2+y^2)^2} \qquad \textrm{und}\\ \frac{\partial z}{\partial y} & = & \frac{x(x^2-y^2)}{(x^2+y^2)^2} \end{eqnarray*}$$

$ \sum\limits_{i=2}^{\infty} \frac{\displaystyle(-1)^i}{\displaystyle i^2}=
\displaystyle{\frac{1}{4}-\frac{1}{9}+\frac{1}{16}-\frac{1}{25}+}~\cdots$

$\sum\limits_{i=2}^{\infty} \frac{\displaystyle(-1)^i}{\displaystyle i^2}=\displaystyle{\frac{1}{4}-\frac{1}{9}+\frac{1}{16}-\frac{1}{25}+}~\cdots$

$ \sum\limits_{i=1}^p \sum\limits_{j=1}^q\sum\limits_{k=1}^r a_{ij}b_{jk}c_{ki}$

$\sum\limits_{i=1}^p \sum\limits_{j=1}^q\sum\limits_{k=1}^r a_{ij}b_{jk}c_{ki}$

$ \sum\limits_{i=1}^p \sum\limits_{j=1}^q\sum\limits_{k=1}^r a_{ij}b_{jk}c_{ki} \qquad
\sum\limits_{{\scriptstyle 1 \le i \le p \atop \scriptstyle 1 \le j \le q} \atop \scriptstyle 1 \le k \le r}
a_{ij} b_{jk} c_{ki}$

$\sum\limits_{{\scriptstyle 1 \le i \le p \atop \scriptstyle 1 \le j \le q} \atop \scriptstyle 1 \le k \le r} a_{ij} b_{jk} c_{ki}$

\begin{eqnarray*}
\sum_{i=0}^{\infty}(-1)^i \frac{1}{2i+1} & = & 1 - \frac{1}{3}+\frac{1}{5}-\cdots\\
& = & \frac{\pi}{4}
\end{eqnarray*}

$$\begin{eqnarray*} \sum_{i=0}^{\infty}(-1)^i \frac{1}{2i+1} & = & 1 - \frac{1}{3}+\frac{1}{5}-\cdots\\ & = & \frac{\pi}{4} \end{eqnarray*}$$

\begin{eqnarray*}
\sum_{i=1}^{\infty}(-1)^{i+1} \frac{1}{i^2} & = & 1-\frac{1}{2^2} + \frac{1}{3^2} - \cdots\\
& = & \frac{\pi^2}{12}
\end{eqnarray*}

$$\begin{eqnarray*} \sum_{i=1}^{\infty}(-1)^{i+1} \frac{1}{i^2} & = & 1-\frac{1}{2^2} + \frac{1}{3^2} - \cdots\\ & = & \frac{\pi^2}{12} \end{eqnarray*}$$

\begin{eqnarray*}
\forall x \in \mathbf{R}:e^{-x} & = &
1 - x + \frac{x^2}{2!} -
\frac{x^3}{3!} + \cdots\\
& = & \sum_{i=0}^{\infty}
(-1)^i\frac{x^i}{i!}
\end{eqnarray*}

$$\begin{eqnarray*} \forall x \in \mathbf{R}:e^{-x} & = & 1 - x + \frac{x^2}{2!} - \frac{x^3}{3!} + \cdots\\ & = & \sum_{i=0}^{\infty} (-1)^i\frac{x^i}{i!} \end{eqnarray*}$$

\begin{eqnarray*}
\forall x \in \mathbf{R}:e^{x} & = &
1 + x + \frac{x^2}{2!} +
\frac{x^3}{3!} + \cdots\\
&=&\sum_{i=0}^{\infty}\frac{x^i}{i!}
\end{eqnarray*}

$$\begin{eqnarray*} \forall x \in \mathbf{R}:e^{x} & = & 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots\\ &=&\sum_{i=0}^{\infty}\frac{x^i}{i!} \end{eqnarray*}$$

$ \displaystyle \lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6} $

$\displaystyle \lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}$

$ \int\limits_{-\infty}^{\infty}\displaystyle{\frac{1}{1 + x^2}} \mathrm{d}x \qquad$
$ \int\limits_0^{\frac{\pi}{3}}\cos x~\mathrm{d}x \qquad$
$ \int\int_D\limits f(x, y) \mathrm{d}x \mathrm{d}y \qquad
\int\!\!\!\int_D\limits f(x, y)\,\mathrm{d}x\,\mathrm{d}y$

$\int\limits_{-\infty}^{\infty}\displaystyle{\frac{1}{1 + x^2}} \mathrm{d}x \qquad$ $\int\limits_0^{\frac{\pi}{3}}\cos x~\mathrm{d}x \qquad$ $\int\int_D\limits f(x, y) \mathrm{d}x \mathrm{d}y \qquad \int\!\!\!\int_D\limits f(x, y)\,\mathrm{d}x\,\mathrm{d}y$

$ \prod_{i=1}^n i = n! \qquad \prod\limits_{i=1}^n i = n! \qquad \prod\nolimits_{i=1}^n i = n!$

$\prod_{i=1}^n i = n! \qquad \prod\limits_{i=1}^n i = n! \qquad \prod\nolimits_{i=1}^n i = n!$

$ \displaystyle{{n \choose k}} = \frac{\displaystyle\prod_{i=1}^n i} {\displaystyle\prod_{i=1}^k i\cdot \prod_{i=1}^{n-k} i}$

$\displaystyle{{n \choose k}} = \frac{\displaystyle\prod_{i=1}^n i} {\displaystyle\prod_{i=1}^k i\cdot \prod_{i=1}^{n-k} i}$

$ \displaystyle \lim_{x \to 0} \frac{\sin x}{x}=1$

$\displaystyle \lim_{x \to 0} \frac{\sin x}{x}=1$

$ \displaystyle \int \frac{\mathrm{d}x} {\sin a x \cos a x} = \frac{1}{a} \ln \tan a x$

$\displaystyle \int \frac{\mathrm{d}x} {\sin a x \cos a x} = \frac{1}{a} \ln \tan a x$

$ \arcsin x = \left[ \arccos \sqrt{1 - x^2}\right]$

$\arcsin x = \left[ \arccos \sqrt{1 - x^2}\right]$

$ \begin{array}{|cccc|}
a_{11} & a_{12} & \cdots & a_{1n} \\\\
a_{21} & a_{22} & \cdots & a_{21} \\\\
\vdots & \vdots & \ddots & \vdots \\\\
a_{m1} & a_{m2} & \cdots & a_{mn}
\end{array}$

$\begin{array}{|cccc|} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{21} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{array}$

$ \left\{\begin{array}{cccc}
\Gamma_{11} & \Gamma_{12} & \cdots & \Gamma_{1n}\\\\
\Gamma_{21} & \Gamma_{22} & \cdots & \Gamma_{2n}\\\\
\vdots & \vdots & \ddots & \vdots\\\\
\Gamma_{m1} & \Gamma_{m2} & \cdots & \Gamma_{mn}
\end{array}\right\}$

$\left\{\begin{array}{cccc} \Gamma_{11} & \Gamma_{12} & \cdots & \Gamma_{1n}\\ \Gamma_{21} & \Gamma_{22} & \cdots & \Gamma_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ \Gamma_{m1} & \Gamma_{m2} & \cdots & \Gamma_{mn} \end{array}\right\}$

$ |x|= \left\{ \begin{array}{ll}
x & \textrm{fuer } x \ge 0\\\\
-x & \textrm{fuer } x < 0\\\\
\end{array}\right\}$

$|x|= \left\{ \begin{array}{ll} x & \textrm{fuer } x \ge 0\\ -x & \textrm{fuer } x < 0\\ \end{array}\right\}$

$ \left(
\begin{array}{c@{}c@{}c}
\begin{array}{|cc|}
\hline
a_{11} & a_{12} \\\\
a_{21} & a_{22} \\\\
\hline
\end{array} & 0 & 0 \\\\
0 & \begin{array}{|ccc|}
\hline
b_{11} & b_{12} & b_{13}\\\\
b_{21} & b_{22} & b_{23}\\\\
b_{31} & b_{32} & b_{33}\\\\
\hline
\end{array} & 0 \\\\
0 & 0 & \begin{array}{|cc|}
\hline
c_{11} & c_{12} \\\\
c_{21} & c_{22} \\\\
\hline
\end{array} \\\\
\end{array}
\right)$

$\left( \begin{array}{c@{}c@{}c} \begin{array}{|cc|} \hline a_{11} & a_{12} \\ a_{21} & a_{22} \\ \hline \end{array} & 0 & 0 \\ 0 & \begin{array}{|ccc|} \hline b_{11} & b_{12} & b_{13}\\ b_{21} & b_{22} & b_{23}\\ b_{31} & b_{32} & b_{33}\\ \hline \end{array} & 0 \\ 0 & 0 & \begin{array}{|cc|} \hline c_{11} & c_{12} \\ c_{21} & c_{22} \\ \hline \end{array} \\ \end{array} \right)$