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:
•  Radius 1/100 radius of contour on which integral is evaluated Method Trapezoidal integration method to use

# Examples

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## Basic Examples(1)

 In[1]:=

Residue of the function about the origin:

 In[2]:=
 Out[2]=