plus the residue at infinity is zero. 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. See also The residue theorem relates a contour integral around some of a function's poles to the sum of their residues Cauchy's integral formula Cauchy's integral theorem Mittag-Leffler's theorem Methods of contour integration Morera's theorem Partial fractions in complex analysis References External links Meromorphic functions