The Laurent series is something like the Taylor series, but with terms with negative exponents, e.g. . The below Laurent Series formula may not be the most practical way to compute the coefficients, usually we will use known formulas, as the example below shows.

## Laurent Series

The Laurent series for a complex function about a point is given by: where

The path of integration is anticlockwise around a closed, rectifiable path containing no self-intersections, enclosing and lying in an annulus in which is holomorphic. The expansion for will then be valid anywhere inside the annulus.

## Example

Consider . This function is holomorphic everywhere except at . Using the Taylor series of the exponential function we get

Note that the residue (coefficient of ) is 2.