numerically finds the residue of expr near the point z=z0.
- To use NResidue, you first need to load the Numerical Calculus Package using Needs["NumericalCalculus`"].
- 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:
Radius 1/100 radius of contour on which integral is evaluated Method Trapezoidal integration method to use