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8-1

$\displaystyle \Int dx\, f(x)\delta\left(g(x)\right)$ (25)

はどのようになるか。

8-1解答

Eq.(24)より

$\displaystyle \Int dx\, f(x)\delta\left(g(x)\right)$ $\displaystyle = \Int dx\,f(x) \sum_{n=1}^N \frac{\delta(x-x_n)}{\left\vert g'(x... ... \Int dx\,\sum_{n=1}^N \frac{f(x) \delta(x-x_n)}{\left\vert g'(x_n)\right\vert}$    
  $\displaystyle =\sum_{n=1}^N \frac{f(x_n)}{\left\vert g'(x_n)\right\vert}$    

を得る。


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著者: 茅根裕司 chinone_at_astr.tohoku.ac.jp