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based on an earlier version of the Wolfram Language.
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NResidue[expr, {z, z0}]
numerically finds the residue of expr near the point z=z0.
  • 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:
Radius1/100radius of contour on which integral is evaluated
MethodTrapezoidalintegration method to use