equation 8.6 eq:cpx-contour-integral

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Supports

• depends_on lemma 8.11 The fundamental $2\pi\ii$ ¶
  • depends_on definition 8.22 Isolated singularities; residue ¶
    • depends_on proposition 8.23 Residue at a simple pole ¶
    • depends_on proposition 17.96 Poles give asymptotics ¶
    • depends_on theorem 8.24 Residue theorem ¶
      • depends_on corollary 17.71 Residue evaluation and causality ¶
        • depends_on corollary 17.76 Heaviside's expansion theorem ¶
        • depends_on proposition 17.77 Poles and stability ¶
      • depends_on example 8.25 A real integral by residues ¶
      • depends_on proposition 17.96 Poles give asymptotics ¶ ↺
      • depends_on proposition 17.61 Mean-square response of a damped resonator ¶
      • depends_on theorem 31.68 Kutta–Joukowski ¶
        • depends_on proposition 31.70 The lift-curve slope of a thin aerofoil ¶
        • depends_on remark 31.69 The Kutta condition, and where the circulation comes from ¶
        • depends_on theorem A.737 The lift-curve slope of the flat plate ¶
      • depends_on theorem 9.26 Structure of the solutions ¶
        • depends_on corollary 9.27 Linear stability ¶
  • depends_on theorem 8.16 Cauchy integral formula ¶
    • depends_on theorem 8.17 Derivatives of all orders; Cauchy estimates ¶
      • depends_on theorem 8.18 Liouville ¶
        • depends_on corollary A.723 Potential of one infinite row ¶
        • depends_on lemma A.608 An entire function with a quadratic bound on its real part ¶
        • depends_on theorem 8.19 Fundamental theorem of algebra ¶
        • depends_on theorem 12.54 The spectrum is compact and non-empty ¶
    • depends_on theorem 8.21 Laurent expansion ¶
      • depends_on definition 8.22 Isolated singularities; residue ¶ ↺
      • depends_on theorem 8.24 Residue theorem ¶ ↺
  • depends_on theorem 8.21 Laurent expansion ¶ ↺
  • depends_on theorem 8.24 Residue theorem ¶ ↺
• depends_on lemma 8.9 ML estimate ¶
  • depends_on example 8.25 A real integral by residues ¶ ↺
  • depends_on lemma 17.70 Jordan's lemma on the Bromwich contour ¶
    • depends_on corollary 17.71 Residue evaluation and causality ¶ ↺
  • depends_on lemma 106.2 Gaussian integrals ¶
    • depends_on lemma 106.1 The short-time kernel ¶
      • depends_on theorem 106.3 Feynman's sum over histories ¶
        • depends_on phenomenon 106.5 The Aharonov–Bohm effect ¶
        • depends_on theorem 106.16 Feynman–Kac ¶
    • depends_on theorem 106.27 The free generating functional and the Feynman propagator ¶
    • depends_on theorem 106.54 The gauge-fixed action ¶
      • depends_on proposition 106.55 Ghosts are required by unitarity ¶
  • depends_on proposition 17.96 Poles give asymptotics ¶ ↺
  • depends_on proposition 106.14 The Feynman contour permits the rotation ¶
  • depends_on theorem 8.16 Cauchy integral formula ¶ ↺
  • depends_on theorem 8.17 Derivatives of all orders; Cauchy estimates ¶ ↺
  • depends_on theorem 8.13 Goursat ¶
  • depends_on theorem 8.20 Taylor expansion ¶
    • depends_on lemma A.608 An entire function with a quadratic bound on its real part ¶ ↺
    • depends_on proposition 8.23 Residue at a simple pole ¶ ↺
    • depends_on theorem A.598 Hudson ¶
    • depends_on theorem 8.21 Laurent expansion ¶ ↺
  • depends_on theorem 17.78 Causality implies dispersion relations ¶
    • depends_on remark 33.10 Fibre anelasticity, and why it biases one method and not the other ¶
    • depends_on remark 28.26 Causality is visible in the susceptibility ¶
    • depends_on remark 28.62 Neither velocity is a speed limit ¶
• depends_on proposition 8.10 Fundamental theorem for contours ¶
  • depends_on theorem 8.13 Goursat ¶ ↺
  • depends_on theorem 8.18 Liouville ¶ ↺