%<PLAINTEXT>
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% $BNL;RJ*M}3X(B : $B1i=,LdBj(B 9-6 $B2rEz(B
% $B:n(B  $B@.(B  $B<T(B : g240916 $B9b>k=E9((B
% $B:n@.G/7nF|(B : /02/12/16
% $BEE;R%a!<%k(B : g240916@mail.ecc.u-tokyo.ac.jp
%
% \mondai{$B:n@.<T(B}{$B:n@.G/7nF|(B}{$BEE;R%a!<%k(B}{$BLdBjHV9f(B}{$BLdBjJ8(B}{$B2rEz(B}
%
\mondai
{g240916 $B9b>k=E9((B}
{/02/12/16}
{g240916@mail.ecc.u-tokyo.ac.jp}
{9-6}
{%----$BLdBjJ8(B----%
$n,\ell$$B$NNL;R?t$GI=$5$l$kF07BJ,I[4X?t$O(B$n-\ell-1$$B$N@a$,$"$k$3$H$r3N$+$a$h!#(B
}
{%----$B2rEzJ8(B----%

$B?eAG86;R$N>l9g$K@.$jN)$D$3$H$r<($9!#!J0lHL$N86;R$G$bF1MM$N$3$H$,4|BT$5$l$k!#!K$^$:(B$(9.23)$$B$h$j!"F07BJ}8~$N@a$K4X$o$k$N$,(BLaguerre$B$NGfB?9`<0$G$"$k$3$H$,$o$+$k!#$D$^$j(BLaguerre$B$NGfB?9`<0$,(B$(0,\infty)$$B$NHO0O$K(B$n-\ell-1$$B8D$NNmE@$r;}$D$3$H$r<($;$P$h$$!#(B
\begin{equation}
P_n(x)=e^{-x}x^n
\end{equation}
$B$H$*$/!#(B$k=0,1,2,...,n-1$$B$KBP$7$F(B
\begin{equation}
P^{(k)}_n(0)=P^{(k)}_n(\infty)=0  \label{9-6-1}
\end{equation}
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\begin{equation}
L_p(x)=\frac{e^x}{p!}P_p(x)
\end{equation}
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$B>e$HF1MM$K$7$F(BRolle$B$NDjM}$r5"G<E*$KMQ$$$l$P!"(B$\displaystyle{\frac{d^q}{dx^q}L_p(x)=0}$$B$N2r$O>/$J$/$H$b(B
$p-q$$B8D$H$J$k!#$7$+$7(B$\displaystyle{\frac{d^q}{dx^q}L_p(x)=0}$$B$O9b!9(B$p-q$$B8D$N<B?t2r$7$+;}$?$J$$$+$i!"(B
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}


