NUMERICAL CALCULUS PACKAGE SYMBOL

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

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Residue of the function about the origin:

 Out[2]=