2.3.4.3 $B=i4|CM6-3&CMLdBj$N7A<02r(B

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Fourier $B78?t(B

$\displaystyle f_n=2\int_0^1 f(x)\sin n\pi x\,\Dx, \quad g_n=2\int_0^1 g(x)\sin n\pi x\,\Dx$

$B$rMQ$$$k$H!"(B

$\displaystyle f(x)=\sum_{n=1}^\infty f_n \sin n\pi x,\quad g(x)=\sum_{n=1}^\infty g_n \sin n\pi x$

$B$G$"$k$+$i!"(B

$\displaystyle v(x,t) =\sum_{n=1}^\infty f_n \sin n\pi x\cos\beta_n t +\sum_{n=1}^\infty g_n \sin n\pi x\frac{k\sin\beta_n t}{\sin\beta_n k}$

$B$,2r$K$J$k$H4|BT$5$l$k!#(B

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Masashi Katsurada
$BJ?@.(B14$BG/(B11$B7n(B29$BF|(B