∮_γ f dz = 2πi Σ Res(f,a_k) for γ enclosing isolated singularities a_k. Evaluates real integrals via contour closure.
Residue theorem
Related concepts
- Cauchy integral formula
- Argument principle
- Picard's theorems (little & great)
- Singular integral (Cauchy principal value)
- Prime number theorem (1896)
- Hartogs extension (1906)
- Kramers–Kronig dispersion: χ'(ω) + iχ''(ω); residue-theorem contour closure
- Phase-locked loop (PLL)
- Kelvin framework: ln(p/p_sat) = 2γ·V_m/(r·R·T) (curvature → vapor-pressure shift)