NResidue


numerically finds the residue of expr near the point .

DetailsDetails

  • To use , 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 in the Laurent expansion of expr.
  • numerically integrates around a small circle centered at the point in the complex plane. will return an incorrect result when the punctured disk is not analytic.
  • 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, can find residues even if the power series cannot be computed.
  • 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