equation 8.2 eq:cpx-exp-series

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Supports

• depends_on proposition 8.4 Euler's formula ¶
  • depends_on lemma A.786 From the half-strip to the half plane ¶
    • depends_on corollary A.788 The two parameters are the same parameter ¶
      • depends_on theorem A.789 Kirchhoff's contraction coefficient ¶
    • depends_on lemma A.787 From the potential strip to the half plane ¶
      • depends_on corollary A.788 The two parameters are the same parameter ¶ ↺
  • 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 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 theorem 9.26 Structure of the solutions ¶
    • 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 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 17.14 Uniformly bounded sine sums ¶
    • depends_on lemma 17.15 A polynomial whose partial sum spikes at the origin ¶
      • depends_on proposition 17.16 An explicit continuous function with a divergent Fourier series ¶