In Wikipedia the definition of a residue of a function $f$ in a point $a$ is a unique value $R$ such that $f(z)-\frac{R}{z-a}$ has an anti derivative in a punctured disk $0<|z-a|<\delta$. How is this equivalent to the $-1$ coefficient of the Laurent series of $f$ around $a$?
2026-03-28 08:27:52.1774686472
The definition of Residue
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Every other term in the Laurent series around $a$ has an anti-derivative. What $-\frac{R}{z-a}$ does in your expression is remove the one term in the Laurent series which doesn't have an anti-derivative, namely the degree $-1$ term.