Residue
Usage Message: Residue[expr, {x, x0}] finds the residue of expr at the point x = x0. Attributes[Residue] = {Protected} Related Functions: Series
Limit
Notes: Residue[expr, {x, x0}] works by evaluating Series[expr, {x, x0, 3}] and
returning the coefficient of x^-1. Residue is currently designed to reject any expressions that contain any functions other than
Plus, Times, Minus, Power, Sin, Cos, ArcCos, ArcSin, Tan, ArcTan,
SinhCosh, ArcSinh, ArcCosh, Tanh, ArcTanh, Log, Cot, ArcCot, Exp, Csc,
Sec, Csch, Sech, Coth, Exp, List, Complex, Rational, Zeta, Gamma, and
Beta. Residue will also reject any expression that does not have a power series expansion around the residue point. Residue
automatically calls Simplify
on the result. Known Bugs: Since Residue uses Series
, it can be expected to have the same capabilities and limitations as the Series
function. If expr does not depend on x, Residue[expr, {x, x0}] will fail because
Series[expr, {x, x0, 3}] returns expr rather than a valid SeriesData
expression. You can correct this problem by adding a rule that causes Residue[expr, {x, x0}] to return zero when expr is a constant.
Additional Online Documentation:
Mathematica 3.0
http://documents.wolfram.com/v3/RefGuide/Residue.html
Mathematica 4.0
http://documents.wolfram.com/v4/RefGuide/Residue.html
Questions or comments? Send email to support@wolfram.com.
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