Revision as of 18:08, 7 November 2007 by imported>Aleksander Stos
In complex analysis, the residue of a complex function f holomorphic in a neighbourhood $\Omega$ of a point
then it can be represented as the Laurent series around this point, that is
with some and coefficients
The coefficient
Although the choice of the coefficient may look arbitrary, it turns out that it is well motivated by the particularly important role played by this number in the theory of complex function.
For example, the residue allows to evaluate path integrals of the function f via the residue theorem. This technique finds many application in real analysis as well.