Editing Residue (complex analysis) (section)

=== Generalization to Laurent series ===
If a function is expressed as a [[Laurent series]] expansion around c as follows:<math display="block">f(z) = \sum_{n=-\infty}^\infty a_n(z-c)^n.</math>Then, the residue at the point c is calculated as:<math display="block">\operatorname{Res}(f,c) = {1 \over 2\pi i} \oint_\gamma f(z)\,dz = {1 \over 2\pi i} \sum_{n=-\infty}^\infty \oint_\gamma a_n(z-c)^n \,dz = a_{-1} </math>using the results from contour integral of a monomial for counter clockwise contour integral <math>\gamma</math> around a point c. Hence, if a [[Laurent series]] representation of a function exists around c, then its residue around c is known by the coefficient of the <math>(z-c)^{-1}</math> term.