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4.7 Fouriereihen

$\displaystyle \int_{a}^{b}$sin$\displaystyle \left(\vphantom{{n \pi x \over a} }\right.$$\displaystyle {n \pi x \over a}$ $\displaystyle \left.\vphantom{{n \pi x \over a} }\right)$sin$\displaystyle \left(\vphantom{{m \pi x \over a} }\right.$$\displaystyle {m \pi x \over a}$ $\displaystyle \left.\vphantom{{m \pi x \over a} }\right)$dx = $\displaystyle {a \over 2}$$\displaystyle \delta_{nm}^{}$ (4.44)

$\displaystyle \sum_{n=1}^{\infty}$cos(nx) = - $\displaystyle {1 \over 2}$ + $\displaystyle \pi$$\displaystyle \sum_{n=-\infty}^{+\infty}$$\displaystyle \delta$(x - 2$\displaystyle \pi$n) (4.45)

$\displaystyle \sum_{n=1}^{\infty}$sin(nx) = - $\displaystyle \pi$$\displaystyle \sum_{n=-\infty}^{-\infty}$$\displaystyle \delta{^\prime}$(x - 2$\displaystyle \pi$n) (4.46)

$\displaystyle \sum_{n=-\infty}^{+\infty}$einx = 2$\displaystyle \pi$$\displaystyle \sum_{n=-\infty}^{+\infty}$$\displaystyle \delta$(x - 2$\displaystyle \pi$n) (4.47)

$\displaystyle \int$Ylmd$\displaystyle \Omega$ = $\displaystyle {1 \over \sqrt{4 \pi}}$4$\displaystyle \pi$$\displaystyle \delta_{l0}^{}$$\displaystyle \delta_{m0}^{}$ (4.48)


Alexander Wagner
2000-04-14