Editing Residue (complex analysis) (section)

===Limit formula for higher-order poles===
More generally, if ''c'' is a [[pole (complex analysis)|pole]] of order ''p'', then the residue of ''f'' around ''z'' = ''c'' can be found by the formula:

: <math> \operatorname{Res}(f,c) = \frac{1}{(p-1)!} \lim_{z \to c} \frac{d^{p-1}}{dz^{p-1}} \left( (z-c)^p f(z) \right). </math>

This formula can be very useful in determining the residues for low-order poles. For higher-order poles, the calculations can become unmanageable, and [[series expansion]] is usually easier. For [[essential singularity|essential singularities]], no such simple formula exists, and residues must usually be taken directly from series expansions.