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| author | daHugen <david.hugentobler@ost.ch> | 2022-07-19 18:35:13 +0200 |
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| committer | daHugen <david.hugentobler@ost.ch> | 2022-07-19 18:35:13 +0200 |
| commit | d56bf4f939d25cea9ac9953b2b0f3237b2dfe8cd (patch) | |
| tree | 93671fdc69442945a0298aa22cb7f4f48234ce54 /buch/papers/lambertw | |
| parent | made some changes and added some text[C (diff) | |
| download | SeminarSpezielleFunktionen-d56bf4f939d25cea9ac9953b2b0f3237b2dfe8cd.tar.gz SeminarSpezielleFunktionen-d56bf4f939d25cea9ac9953b2b0f3237b2dfe8cd.zip | |
added some equations and made some changes
Diffstat (limited to 'buch/papers/lambertw')
| -rw-r--r-- | buch/papers/lambertw/teil4.tex | 14 |
1 files changed, 10 insertions, 4 deletions
diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index e0f7731..6184369 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -237,10 +237,16 @@ Leitet man die Funktion \eqref{lambertw:funkLoes} nach x ab und setzt die Anfang \frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi} &= \eta \\ - x\left(t\right) - &= - \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \\ \frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi} &= - \left(\frac{x}{x_0}\right)^2 + \left(\frac{x}{x_0}\right)^2 \\ + x\left(t\right) + &= + \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \end{align*} +\begin{equation} + y(t) + = + \frac{1}{4}\left(\left(y_0+r_0\right)\frac{W\left(\chi\cdot e^{\chi\ -\ \frac{4t}{r_0-y_0}}\right)}{\chi}+\left(r_0-y_0\right)\cdot\mathrm{ln}\ \left(\frac{W\left(\chi\cdot e^{\chi\ -\ \frac{4t}{r_0-y_0}}\right)}{\chi}\right)-r_0+3y_0\right) + \label{lambertw:funkNachT} +\end{equation} |