Complex Residue

Author

Eric W. Weisstein
April 15, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/ComplexAnalysis/ComplexResidue.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ComplexResidue.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Code and description by
Todd Rowland

Figure

The diagram shows a suitable contour for which to define the residue of function with the poles given as black dots.

<<Graphics`Colors`;
<<Graphics`Arrow`;

Clear[aa,bb];
aa={1,0};
bb={Cos[Pi/3],Sin[Pi/3]};
Show[Graphics[{PointSize[.03],Table[Point[aa i + bb j],{i,-2,2},{j,-2,2}],
Red,
Line[Table[.2{Cos[x],Sin[x]},{x,0,2Pi,Pi/20}]],
Arrow[{.03,.2},{-.07,.2}],
Arrow[{-.03,-.2},{.07,-.2}]
}],PlotRange->1.4{{-1,1},{-1,1}},AspectRatio->Automatic]