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--- spielplatz:mathematische-formeln-anleitung [2019/04/14 08:55] – alte Version wiederhergestellt (2019/04/14 10:52) wi
+++ spielplatz:mathematische-formeln-anleitung [2023/04/18 09:12] (aktuell) – [Mathematische Formeln in Dokuwiki] wi
@@ Zeile 3: / Zeile 3: @@
 Zusammengestellt von M. Wilfling, HTBLA Kaindorf
-$xxx$
+$ \frac{1}{x} $
 Wer möchte seine Wiki Seiten, die mathematische Formeln enthalten, professionell gestalten?
@@ Zeile 90: / Zeile 90: @@
 ==== Sonderzeichen und Griechische Buchstaben ====
-<code>$ \mathrm{A}\mathrm{B}\Gamma\Delta\mathrm{E}\mathrm{Z}\mathrm{H}\Theta\mathrm{I}\mathrm{K}\Lambda
+  $ \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$</code>
+  \mathrm{M}\mathrm{N}\Xi\mathrm{O}\Pi\mathrm{P}\Sigma\mathrm{T}\Phi\mathrm{X}\mathrm{Y}\Psi\Omega$
-$ \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$
+$ \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$
-<code>$\alpha\beta\gamma\delta\epsilon\zeta\eta\theta\iota\kappa\lambda\mu\nu\xi\mathrm{o}\pi\rho\sigma\tau\phi\chi\upsilon\psi\omega$</code>
+  $ \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$
-<code>$\varepsilon \quad \vartheta \quad \varpi \quad \varrho \quad \varsigma \quad \varphi$</code>
+  $\varepsilon \quad \vartheta \quad \varpi \quad \varrho \quad \varsigma \quad \varphi$
 $ \varepsilon \quad \vartheta \quad \varpi \quad \varrho \quad \varsigma \quad \varphi$
-<code>$\aleph\quad\Re\quad\Im\quad\partial\quad\infty\quad\forall\quad\exists\quad\neg\quad\in\quad\heartsuit$</code>
+  $\aleph\quad\Re\quad\Im\quad\partial\quad\infty\quad\forall\quad\exists\quad\neg\quad\in\quad\heartsuit$
 $ \aleph\quad\Re\quad\Im\quad\partial\quad\infty\quad\forall\quad\exists\quad\neg\quad\in\quad\heartsuit$
-<code>$ \forall \varepsilon>0:|f(x_1)-f(x_2)| < \varepsilon\quad\exists\eta: |x_1-x_2|<\eta$</code>
+  $ \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}$
 ==== Klammern ====
-<code>$ ( ~ \lbrack ~ \lbrace ~ [ ~ \lfloor ~ \langle ~ \{ ~ \lceil$</code>
+  $ ( ~ \lbrack ~ \lbrace ~ [ ~ \lfloor ~ \langle ~ \{ ~ \lceil$
 $ ( ~ \lbrack ~ \lbrace ~ [ ~ \lfloor ~ \langle ~ \{ ~ \lceil$
-<code>$) ~ \rbrack ~ \rbrace ~ ]~ \rfloor ~ \rangle ~ \} ~  \rceil$</code>
+  $ ) ~ \rbrack ~ \rbrace ~ ]~ \rfloor ~ \rangle ~ \} ~  \rceil$
-$) ~ \rbrack ~ \rbrace ~ ]~ \rfloor ~ \rangle ~ \} ~  \rceil$
+$ ) ~ \rbrack ~ \rbrace ~ ]~ \rfloor ~ \rangle ~ \} ~  \rceil$
-<code>$ \Bigl( (x+1) (x-1)\Bigr) ^2$</code>
+  $ \Bigl( (x+1) (x-1)\Bigr) ^2$
 $ \Bigl( (x+1) (x-1)\Bigr) ^2$
-<code>$ \left( (x+1) (x-1)\right) ^2$</code>
+  $ \left( (x+1) (x-1)\right) ^2$
 $ \left( (x+1) (x-1)\right) ^2$
-<code>$ 1 + \left(\frac{1}{1-x^2}\right)$</code>
+  $ 1 + \left(\frac{1}{1-x^2}\right)$
 $ 1 + \left(\frac{1}{1-x^2}\right)$
-<code>$ \underbrace{\overbrace{a + b + \cdots +z}^{26} + \overbrace{A + B + \cdots+Z}^{26}}_{52}$</code>
+  $ \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}$
-<code>$ \overline{m+n} \qquad \underline{m+n}$</code>
+  $ \overline{m+n} \qquad \underline{m+n}$
 $ \overline{m+n} \qquad \underline{m+n}$
 ==== Operatoren ====
-<code>$x = y > z \qquad x := y \qquad x \le y \ne z $</code>
+  $x = y > z \qquad x := y \qquad x \le y \ne z $
 $x = y > z \qquad x := y \qquad x \le y \ne z$
-<code>$x \sim y \simeq z \qquad x \equiv y \not\equiv z \qquad x \subset y \subseteq z$</code>
+  $x \sim y \simeq z \qquad x \equiv y \not\equiv z \qquad x \subset y \subseteq z$
 $x \sim y \simeq z \qquad x \equiv y \not\equiv z \qquad x \subset y \subseteq z$
-<code>$x + y - z \qquad x * y / z \qquad x \times y \cdot z$</code>
+  $x + y - z \qquad x * y / z \qquad x \times y \cdot z$
 $x + y - z \qquad x * y / z \qquad x \times y \cdot z$
-<code>$x \circ y \bullet z \qquad x \cup y \cap z \qquad x \sqcup y \sqcap z$</code>
+  $x \circ y \bullet z \qquad x \cup y \cap z \qquad x \sqcup y \sqcap z$
 $x \circ y \bullet z \qquad x \cup y \cap z \qquad x \sqcup y \sqcap z$
-<code>$x \vee y \wedge z\qquad x \pm y \mp z$</code>
+  $x \vee y \wedge z\qquad x \pm y \mp z$
 $x \vee y \wedge z\qquad x \pm y \mp z$
 ==== Akzente ====
-<code>$ \hat a\qquad\check b\qquad\tilde c \qquad \acute d \qquad \grave$</code>
+  $ \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$
+$ \hat a \qquad \check b \qquad \tilde c \qquad \acute d \qquad \grave e$
-<code>$ \dot f\qquad\ddot g\qquad\breve h \qquad \bar k \qquad \vec l$</code>
+  $ \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$
-<code>$ \hat\imath \qquad \check\jmath$</code>
+  $ \hat\imath \qquad \check\jmath$
 $ \hat\imath \qquad \check\jmath$
-<code>$ \widehat x \qquad \widehat{xy} \qquad \widehat{xyz}$</code>
+  $ \widehat x \qquad \widehat{xy} \qquad \widehat{xyz}$
 $ \widehat x \qquad \widehat{xy} \qquad \widehat{xyz}$
-<code>$ \widetilde x \qquad \widetilde{xy} \qquad \widetilde{xyz}$</code>
+  $ \widetilde x \qquad \widetilde{xy} \qquad \widetilde{xyz}$
 $ \widetilde x \qquad \widetilde{xy} \qquad \widetilde{xyz}$
 ==== Vektoren ====
-<code>$ \alpha \cdot(\vec x + \vec y) = \alpha \cdot \vec x + \alpha \cdot \vec y$</code>
+  $ \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$
-<code>$ \vec x \cdot (\vec y \cdot \vec z) \not=(\vec x\cdot\vec y)\cdot \vec z$</code>
+  $ \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$
-<code>$ \vec x\times (\vec y\times \vec z) \not= (\vec x \times \vec y) \times \vec z$</code>
+  $ \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$
 ==== Pfeile ====
-<code>$\leftarrow \qquad \Leftarrow \qquad \leftrightarrow \qquad
+  $ \leftarrow \qquad \Leftarrow \qquad \leftrightarrow \qquad
-\Leftrightarrow \qquad \uparrow\qquad\downarrow\qquad\nearrow$</code>
+  \Leftrightarrow \qquad \uparrow\qquad\downarrow\qquad\nearrow$
-$\leftarrow \qquad \Leftarrow \qquad \leftrightarrow \qquad \Leftrightarrow \qquad \uparrow\qquad\downarrow\qquad\nearrow$
+$ \leftarrow \qquad \Leftarrow \qquad \leftrightarrow \qquad \Leftrightarrow \qquad \uparrow\qquad\downarrow\qquad\nearrow$
-<code>$\longleftarrow\qquad\leftharpoonup \qquad \mapsto \qquad \leadsto$</code>
+  $\longleftarrow\qquad\leftharpoonup \qquad \mapsto \qquad \leadsto$
-$\longleftarrow\qquad\leftharpoonup \qquad \mapsto \qquad \leadsto$
+$ \longleftarrow\qquad\leftharpoonup \qquad \mapsto \qquad \leadsto$
-<code>$(\mathcal{A} \Rightarrow \mathcal{B}) \Longleftrightarrow
+  $ (\mathcal{A} \Rightarrow \mathcal{B}) \Longleftrightarrow
-(\lnot \mathcal{B} \Rightarrow \lnot \mathcal{A})$</code>
+  (\lnot \mathcal{B} \Rightarrow \lnot \mathcal{A})$
-$(\mathcal{A} \Rightarrow \mathcal{B}) \Longleftrightarrow (\lnot \mathcal{B} \Rightarrow \lnot \mathcal{A})$
+$ (\mathcal{A} \Rightarrow \mathcal{B}) \Longleftrightarrow (\lnot \mathcal{B} \Rightarrow \lnot \mathcal{A})$
-<code>$(\mathcal{A} \Longleftrightarrow \mathcal{B}) \Longleftrightarrow
+  $(\mathcal{A} \Longleftrightarrow \mathcal{B}) \Longleftrightarrow
-(\mathcal{A}\Rightarrow \mathcal{B}) \wedge (\mathcal{B}\Rightarrow\mathcal{A})$
+  (\mathcal{A}\Rightarrow \mathcal{B}) \wedge (\mathcal{B}\Rightarrow\mathcal{A})$
-</code>
-$(\mathcal{A} \Longleftrightarrow \mathcal{B}) \Longleftrightarrow
+$ (\mathcal{A} \Longleftrightarrow \mathcal{B}) \Longleftrightarrow
 (\mathcal{A}\Rightarrow \mathcal{B}) \wedge (\mathcal{B}\Rightarrow\mathcal{A})$
 ==== Schriftartwechsel ====
-<code>$ \forall x\in\mathbf{R}: x^2\ge0$</code>
+  $ \forall x\in\mathbf{R}: x^2\ge0$
 $ \forall x\in\mathbf{R}: x^2\ge0$
 <code>\begin{eqnarray*}
@@ Zeile 184: / Zeile 188: @@
 \end{eqnarray*}
 ==== Indizes und Hochstellung ====
-<code>$ \displaystyle a_i \qquad a_{i_j} $</code>
+  $ \displaystyle a_i \qquad a_{\displaystyle i_j} $
 $ \displaystyle a_i \qquad a_{\displaystyle i_j} $
-<code>$ \displaystyle a^{\displaystyle i} \qquad a^{\displaystyle i^j} $</code>
+  $ \displaystyle a^{\displaystyle i} \qquad a^{\displaystyle i^j} $
 $ \displaystyle a^{\displaystyle i} \qquad a^{\displaystyle i^j} $
-<code>$ _1x_2 \qquad x^3_4 \qquad a^{b^\alpha_\beta}_{c^\gamma_\delta} \qquad F^1_2 \qquad F{}^1_2$</code>
+  $ _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$
-<code>$ \displaystyle _1x_2 = \sqrt{\left(\frac{p}{2}\right)^2-q}$</code>
+  Vergleiche $ \displaystyle _1x_2 = \sqrt{\left(\frac{p}{2}\right)^2-q}$
-$ \displaystyle _1x_2 = -\frac{p}{2}\pm \sqrt{\left(\frac{p}{2}\right)^2-q}$
+  mit  $ _1x_2 = -\frac{p}{2}\pm \sqrt{\left(\frac{p}{2}\right)^2-q}$ !
+Vergleiche $ \displaystyle _1x_2 = \sqrt{\left(\frac{p}{2}\right)^2-q}$
+mit  $ _1x_2 = -\frac{p}{2}\pm \sqrt{\left(\frac{p}{2}\right)^2-q}$ !
 ==== Brüche ====
-<code>$ \frac{1}{2} \qquad \frac{n+1}{3}$</code>
+  $ \displaystyle \frac{1}{2} \qquad \frac{n+1}{3}$
 $ \displaystyle \frac{1}{2} \qquad \frac{n+1}{3}$
-<code>$ \frac{x+y^2}{m+1} \qquad \frac{x+y^2}{m} + 1 \qquad x + \frac{y^2}{m}+1$</code>
+  $ \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$
-<code>$x + \frac{y^2}{m+1} \qquad x + y^\frac{2}{m+1}$</code>
+  $x + \frac{\displaystyle y^2}{\displaystyle m+1} \qquad x + y^\frac{\displaystyle 2}{\displaystyle m+1}$
 $x + \frac{\displaystyle y^2}{\displaystyle m+1} \qquad x + y^\frac{\displaystyle 2}{\displaystyle m+1}$
-<code>$ \displaystyle x + \frac{y^2}{m+1} \qquad x + y^\frac{2}{m+1}$</code>
+  $ \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}$
-<code>$ \displaystyle \frac{\frac{x}{y}}{2} \qquad \frac{x}{\frac{y}{2}}$</code>
+  $ \displaystyle \frac{\frac{x}{y}}{2} \qquad \frac{x}{\frac{y}{2}}$
 $ \displaystyle \frac{\frac{x}{y}}{2} \qquad \frac{x}{\frac{y}{2}}$
-<code>$x_0 + \frac{1}{x_1 +
+  $x_0 + \frac{1}{x_1 +
-\frac{1}{x_2 +
+  \frac{1}{x_2 +
-\frac{1}{x_3 +
+  \frac{1}{x_3 +
-\frac{1}{x_4}}}}$</code>
+  \frac{1}{x_4}}}}$
 $x_0 + \frac{1}{x_1 +
 \frac{1}{x_2 +
 \frac{1}{x_3 +
 \frac{1}{x_4}}}}$
-<code>
-$ \displaystyle x_0+\frac{1}{\displaystyle x_1 + \frac{\strut 1}{\displaystyle x_2 + \frac{\strut 1}{\displaystyle x_3 +
+  $ \displaystyle x_0 + \frac{1}{\displaystyle x_1 +
-\frac{\strut 1}{\displaystyle x_4}}}}$
+  \frac{\strut 1}{\displaystyle x_2 +
-</code>
+  \frac{\strut 1}{\displaystyle x_3 +
+  \frac{\strut 1}{\displaystyle x_4}}}}$
 $ \displaystyle x_0+\frac{1}{\displaystyle x_1 +
@@ Zeile 223: / Zeile 230: @@
 \frac{\strut 1}{\displaystyle x_4}}}}$
 ==== Wurzeln ====
-<code>$ \sqrt 2 \qquad \sqrt{\displaystyle x^2-y^2} \qquad \sqrt{\alpha^2 + \beta^2 - \gamma^2}$</code>
+  $ \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}$
-<code>$ \sqrt[3]{2} \qquad \sqrt[n]{\sqrt\alpha + \sqrt\beta} \qquad \sqrt[n+1]{a^n + b^n}$</code>
+  $ \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}$
-<code>$ \sqrt a +\sqrt b +\sqrt c \qquad \sqrt{\mathstrut a} + \sqrt{\mathstrut b} + \sqrt{\mathstrut c}$</code>
+  $ \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}$
-<code>$ \sqrt{1+ \sqrt{1+ \sqrt{1+ \sqrt{1+ \sqrt{1 + \sqrt{1+x}}}}}}$</code>
+  $ \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}}}}}}$
 ==== Binominalkoeffizienten ====
-<code>${n \choose 2} \qquad {n+1 \choose k} \qquad \frac{\displaystyle{n \choose k}}{\displaystyle 2}$</code>
+  ${n \choose 2} \qquad {n+1 \choose k} \qquad \frac{\displaystyle{n \choose k}}{\displaystyle 2}$
 ${n \choose 2} \qquad {n+1 \choose k} \qquad \frac{\displaystyle{n \choose k}}{\displaystyle 2}$
-<code>${x \atop a+b} \qquad {n \atop k+1}$</code>
+  ${x \atop a+b} \qquad {n \atop k+1}$
 ${x \atop a+b} \qquad {n \atop k+1}$
-<code>$ \displaystyle \sum_{{\scriptstyle 1 \le i \le p \atop \scriptstyle 1 \le j \le q}} a_{ij} b_{ji}$</code>
+  $ \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}$
 ==== Limes, Ableitungen ====
-<code>$\displaystyle f\prime(x) = \lim_{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}$</code>
+  $ \displaystyle f\prime(x) = \lim_{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}$
-$\displaystyle f\prime(x) = \lim_{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}$
+$ \displaystyle f\prime(x) = \lim_{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}$
 <code>\begin{eqnarray*}
 f(x) & = & \cos x \\
@@ Zeile 251: / Zeile 259: @@
 f’’(x) & = & -\cos x \\
 \end{eqnarray*}
 <code>\begin{eqnarray*}
 h(x) & = & f(x) \cdot g(x)\\
@@ Zeile 259: / Zeile 268: @@
 \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*}
 <code>\begin{eqnarray*}
 \mathbf{x} & = & \frac{1}{2} \mathbf{k} \cdot t^2 + \mathbf{v_0} \cdot t + \mathbf{x_0}\\
@@ Zeile 264: / Zeile 274: @@
 \ddot \mathbf{x} & = & \mathbf{k}
 \end{eqnarray*}</code>
 <code>\begin{eqnarray*}
 \mathbf{x} & = & \frac{1}{2} \mathbf{k} \cdot t^2 + \mathbf{v_0} \cdot t + x_0\\
@@ Zeile 274: / Zeile 285: @@
 \ddot{\mathbf{x}} & = & \mathbf{k}
 \end{eqnarray*}
 <code>\begin{eqnarray*}
 z (x, y) & = & xy\\
@@ Zeile 284: / Zeile 296: @@
 \frac{\partial z}{\partial y} & = & x
 \end{eqnarray*}
 <code>\begin{eqnarray*}
 z (x, y) & = & \frac{xy}{x^2+y^2} \quad(\forall x,y:x^2+y^2\not=0)\\
@@ Zeile 295: / Zeile 308: @@
 \end{eqnarray*}
 ==== Summen ====
-<code>$ \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$</code>
+  \sum\limits_{i=2}^{\infty} \frac{\displaystyle(-1)^i}{\displaystyle i^2}=
+  \displaystyle{\frac{1}{4}-\frac{1}{9}+\frac{1}{16}-\frac{1}{25}+}~\cdots$
 $ \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$
 <code>$ \sum\limits_{i=1}^p \sum\limits_{j=1}^q\sum\limits_{k=1}^r a_{ij}b_{jk}c_{ki}$</code>
 $ \sum\limits_{i=1}^p \sum\limits_{j=1}^q\sum\limits_{k=1}^r a_{ij}b_{jk}c_{ki}$
@@ Zeile 375: / Zeile 391: @@
 $ \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$
-<code>$ \prod_{i=1}^n i = n! \qquad \prod\limits_{i=1}^n i = n! \qquad \prod\nolimits_{i=1}^n i = n!$</code>
+  $ \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!$
-<code>$ \displaystyle{{n \choose k}} = \frac{\displaystyle\prod_{i=1}^n i} {\displaystyle\prod_{i=1}^k i\cdot \prod_{i=1}^{n-k} i}$</code>
+  $ \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}$
 ==== Funktionen ====
-<code>$ \displaystyle \lim_{x \to 0} \frac{\sin x}{x}=1$</code>
+  $ \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$
-<code>$ \arcsin x = \left[ \arccos \sqrt{1 - x^2}\right]$</code>
+  $ \arcsin x = \left[ \arccos \sqrt{1 - x^2}\right]$
 $ \arcsin x = \left[ \arccos \sqrt{1 - x^2}\right]$
 ==== Matrizen ====

spielplatz/mathematische-formeln-anleitung.1555232103.txt.gz · Zuletzt geändert: 2019/04/14 08:55 von wi

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