aboutsummaryrefslogtreecommitdiffstats
path: root/vorlesungen/slides/hermite/loesung.tex
diff options
context:
space:
mode:
authorenezerdem <105669082+enezerdem@users.noreply.github.com>2022-06-07 15:13:30 +0200
committerGitHub <noreply@github.com>2022-06-07 15:13:30 +0200
commit5d18eabd6477d0d4d2ace3ebe1ba2a1b8b21b0de (patch)
tree8d5e0a1adf3881ff1e9730df405264f8b15a15f4 /vorlesungen/slides/hermite/loesung.tex
parentMerge pull request #8 from AndreasFMueller/master (diff)
parentindex entries added (diff)
downloadSeminarSpezielleFunktionen-5d18eabd6477d0d4d2ace3ebe1ba2a1b8b21b0de.tar.gz
SeminarSpezielleFunktionen-5d18eabd6477d0d4d2ace3ebe1ba2a1b8b21b0de.zip
Merge pull request #9 from AndreasFMueller/master
synch
Diffstat (limited to '')
-rw-r--r--vorlesungen/slides/hermite/loesung.tex19
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}