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MATHEMATICA TUTORIAL

Residues

tells you what the value of expr is when x tends to

. When this value is infinite, it is often useful instead to know the residue of expr when x equals

. The residue is given by the coefficient of

in the power series expansion of expr about the point

Residue[expr,{x,x₀}]

the residue of expr when x equals

Computing residues.

The residue here is equal to 1.

Out[1]=

The residue here is zero.

Out[2]=

Residues can be computed at the point at infinity.

Out[3]=