The expression expr must be numeric when its argument x is numeric.
The residue is defined as the coefficient of (z-z0)-1 in the Laurent expansion of expr.
NResidue numerically integrates around a small circle centered at the point z0 in the complex plane. NResidue will return an incorrect result when the punctured disk is not analytic.
NResidue is unable to recognize small numbers that should in fact be zero. Chop is often needed to eliminate these spurious residuals.
Although Residue usually needs to be able to evaluate power series at a point, NResidue can find residues even if the power series cannot be computed.
NResidue has the same options as NIntegrate, with the following additions and changes:
EXAMPLES
Basic Examples 
Scope 