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Next: 3.2 Die -Funktion als Up: 3. Die Dirac'sche -Funktion Previous: 3. Die Dirac'sche -Funktion   Inhalt

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