NumericalCalculus`
NumericalCalculus`

NResidue

NResidue[expr,{z,z0}]

numerically finds the residue of expr near the point z=z0.

Details

  • 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:
  • Radius1/100radius of contour on which integral is evaluated
    MethodTrapezoidalintegration method to use

Examples

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Basic Examples  (1)

In[1]:=
Click for copyable input

Residue of the function about the origin:

In[2]:=
Click for copyable input
Out[2]=

Scope  (2)

Generalizations & Extensions  (1)

Options  (3)

Applications  (2)

Properties & Relations  (1)

Possible Issues  (1)

See Also

NSeries  Residue  NLimit  ND

Tutorials