If we say that $$ f(z)=\sum_{n=-\infty}^{\infty} c_{n}\left(z-z_{0}\right)^{n} $$ was the Laurent expansion of $f$ around a second order pole $z_{0}$ of $f$, can you then calculate the residue $Res_{z_{0}}f(z)^2$ of $f^{2}$ at $z_{0}$ from the Laurent coefficients $c_{-2}, c_{-1}, c_{0}$ and $c_{1}$ ?
2026-04-04 06:37:11.1775284631
Residue by Laurent coefficients
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