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author | Nicolas Tobler <nicolas.tobler@ost.ch> | 2022-08-03 20:37:12 +0200 |
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committer | Nicolas Tobler <nicolas.tobler@ost.ch> | 2022-08-03 20:37:12 +0200 |
commit | e08392d4bacb9a54c3ab755fa6445514749b608f (patch) | |
tree | 67af5a4a6ed541b1b425de89fd05c2a74a265571 /vorlesungen/slides/hermite/loesung.tex | |
parent | improved Einleitung (diff) | |
parent | Merge pull request #39 from NaoPross/master (diff) | |
download | SeminarSpezielleFunktionen-e08392d4bacb9a54c3ab755fa6445514749b608f.tar.gz SeminarSpezielleFunktionen-e08392d4bacb9a54c3ab755fa6445514749b608f.zip |
Merge branch 'master' of https://github.com/AndreasFMueller/SeminarSpezielleFunktionen
Diffstat (limited to '')
-rw-r--r-- | vorlesungen/slides/hermite/loesung.tex | 19 |
1 files changed, 14 insertions, 5 deletions
diff --git a/vorlesungen/slides/hermite/loesung.tex b/vorlesungen/slides/hermite/loesung.tex index 7d4741f..68ee32e 100644 --- a/vorlesungen/slides/hermite/loesung.tex +++ b/vorlesungen/slides/hermite/loesung.tex @@ -20,36 +20,45 @@ P(t)e^{-\frac{t^2}2} \] in geschlossener Form angeben? \end{block} +\uncover<2->{% \begin{block}{``Hermite-Antwort''} \[ \int H_n(x)e^{-x^2}\,dx \] kann genau für $n>0$ in geschlossener Form angegeben werden. -\end{block} +\end{block}} \end{column} \begin{column}{0.48\textwidth} +\uncover<3->{% \begin{block}{Allgemein} \begin{align*} \int P(x)e^{-x^2}\,dx -&= -\int \sum_{k=0}^n a_kH_k(x)e^{-x^2}\,dx +&\uncover<4->{= +\int \sum_{k=0}^n a_kH_k(x)e^{-x^2}\,dx} \\ +\uncover<5->{ &= \sum_{k=0}^n a_k \int H_k(x)e^{-x^2}\,dx +} \\ +\uncover<6->{ &= a_0\operatorname{erf}(x) + C +} \\ +\uncover<6->{ &\hspace*{2mm} + \sum_{k=1}^n a_k\int H_k(x)e^{-x^2}\,dx +} \end{align*} -\end{block} +\end{block}} +\uncover<7->{% \begin{theorem} Das Integral von $P(x)e^{-x^2}$ ist genau dann elementar darstellbar, wenn $a_0=0$ -\end{theorem} +\end{theorem}} \end{column} \end{columns} \end{frame} |