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Beskonačna membrana s rupom u obliku kruga

Sada moramo izbaciti rješenja $ r^n$ i $ \ln r,$ pa sličnim rezoniranjem dolazimo do rješenja

$\displaystyle u(r,\varphi) = C_{10} + \sum_{n=1}^{\infty} \frac{1}{r^n}\,\left(C_{1n}\,\cos n\varphi + C_{2n}\,\sin n\varphi\right),$

gdje je, koristeći rubni uvjet,

$\displaystyle C_{10} = \frac{1}{2\,\pi}\,\int_{-\pi}^{\pi}\,\alpha(\varphi)\,d\... ... \frac{R^n}{\pi}\,\int_{-\pi}^{\pi}\,\alpha(\varphi)\,\cos n\varphi\,d\varphi,$

$\displaystyle C_{2n} = \frac{R^n}{\pi}\,\int_{-\pi}^{\pi}\,\alpha(\varphi)\,\sin n\varphi\,d\varphi.$

\includegraphics{m3bezkruga.eps}


2001-10-26