Serie di Laurent: differenze tra le versioni
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→Teorema di Laurent: correzione nella dimostrazione |
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Riga 43:
<math>\begin{align}
f(z)&=\frac{1}{2 \pi i}\left(\oint_{\gamma_{1}}\frac{f_{\zeta}}{(\zeta-z_{0})}\sum_{n=0}^{\infty}\left(\frac{z-z_{0}}{\zeta-z_{0}}\right)^{n}d\zeta+\oint_{\gamma_{2}}\frac{f_{\zeta}}{(z-z_{0})}\sum_{k=0}^{\infty}\left(\frac{\zeta-z_{0}}{z-z_{0}}\right)^{k}d\zeta\right)=\\
&=\frac{1}{2 \pi i}\left(\sum_{n=0}^{\infty}\oint_{\gamma_{1}}\frac{f_{\zeta}}{(\zeta-z_{0})^{n+1}}(z-z_{0})^{n}d\zeta+\sum_{k=
&=\frac{1}{2 \pi i}\left(\sum_{n=0}^{\infty}\oint_{\gamma_{1}}\frac{f_{\zeta}}{(\zeta-z_{0})^{n+1}}(z-z_{0})^{n}d\zeta+\sum_{n=-\infty}^{-1}\oint_{\gamma_{2}}\frac{f_{\zeta}}{(\zeta-z_{0})^{n+1}}(z-z_{0})^{n}d\zeta\right)
\end{align}</math>
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