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3.1 Limesdarstellungen

$\displaystyle \delta$ (x) = $\displaystyle {1 \over \pi}$ $\displaystyle \lim_{\varepsilon\rightarrow 0}^{}$ $\displaystyle {\varepsilon \over {x^2+\varepsilon^2}}$ =

(3.3)

$\displaystyle {1 \over {2 \sqrt{\pi}}}$ $\displaystyle \lim_{\varepsilon\rightarrow 0}^{}$ $\displaystyle {1 \over {\sqrt{\varepsilon}}}$ exp $\displaystyle {({-x^2 \over {4\varepsilon}})}$ =

(3.4)

= $\displaystyle {1 \over \pi}$ $\displaystyle \lim_{\nu\rightarrow \infty}^{}$ $\displaystyle {\sin(\nu x) \over x}$ = $\displaystyle {1 \over \pi}$ $\displaystyle \lim_{\nu\rightarrow \infty}^{}$ $\displaystyle {{\sin^2(\nu x)} \over {\nu x^2}}$

(3.5)

Alexander Wagner
2000-04-14