structural:expansion, structural:scholar_edition, information:highlighting, quality:correction
Series methods

If parts or all of a function can be expanded into a Taylor series or Laurent series, which may be possible if the parts or the whole of the function has a standard series expansion, then calculating the residue is significantly simpler than by other methods. The residue of the function is simply given by the coefficient of (z − c) − 1 {\displaystyle (z-c)^{-1}} in the Laurent series expansion of the function.