Mathematics · Advanced university
Residue at a simple pole · formula reference
The numerator is analytic near a and the pole is simple.
Formula
The numerator is analytic near a and the pole is simple.
Res[p(z)/(z−a),a] = p(a)
Worked example
Find the residue at z = 2 of f(z) = (2z² + 8)/(z − (2)). Round the final result to 4 decimal places if needed.
Multiply by z − (2) and take the limit z → 2. The remaining polynomial is evaluated at the pole.
16
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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