Residue Formula
Source lecture(s): PHY622 Lec4
Physical Meaning
Evaluates closed contours by summing local pole strengths.
Variable Definitions
| Symbol | Meaning |
|---|---|
| \(\text{Res}\) | residue at pole |
| \(z_k\) | pole locations |
Assumptions
Isolated singularities inside contour.
Derivation
Deform to small circles around poles; each contributes \(2\pi i\cdot\text{Res}\).
Applications
Evaluating real integrals, summing series, inverse Laplace transforms.
Connections to Other Equations
- cauchy-theorem
- cauchy-integral-formula