Laurent Series Calculator
Calculate Laurent series expansion coefficients for complex functions around a point.
Complex Function f(z) = u + iv
Expansion Point z0
Laurent Series
f(z) = sum a_n (z - z0)^n
n from -infinity to infinity
Residue (a_-1)
1.0000 + 0.0000i
Laurent Coefficients
a_-11.0000 + 0.0000i
-nPrincipal Terms
1
+nAnalytic Terms
0
Series Structure
Principal part: Terms with n < 0 (singularity info)
Analytic part: Terms with n >= 0 (Taylor series)
Residue: Coefficient a_-1 for contour integrals
About Laurent Series
Definition
A Laurent series is a generalization of the Taylor series that allows negative powers. It represents a function in an annular region around a singularity.
Applications
- Classifying singularities
- Computing residues
- Asymptotic analysis
- Evaluating contour integrals