theorem A.789 Kirchhoff's contraction coefficient

open in the book · appendices/A-long-proofs.tex:38717 · p. 3183

Rests on

depends_on corollary A.788 The two parameters are the same parameter ¶
- depends_on lemma A.786 From the half-strip to the half plane ¶
  - depends_on definition 8.3 Exponential, sine, cosine ¶
    - depends_on proposition 7.48 Ratio test ¶
      - depends_on proposition 7.47 Comparison; absolute convergence ¶
      - depends_on proposition 7.46 Geometric series ¶
      - depends_on theorem 7.8 Cauchy criterion ¶
      - proves proof ch:05-real-analysis@proof-29 ¶
    - depends_on theorem 7.50 Power series; radius of convergence ¶
      - depends_on axiom 7.1 Completeness of $\R$ ¶
      - depends_on proposition 7.47 Comparison; absolute convergence ¶ ↺
      - depends_on proposition 7.46 Geometric series ¶ ↺
      - proves proof ch:05-real-analysis@proof-31 ¶
  - depends_on lemma A.785 The hodograph image ¶
    - depends_on definition 8.3 Exponential, sine, cosine ¶ ↺
    - depends_on equation A.1327 eq:app-free-streamline-jet-omega ¶
    - depends_on equation A.1328 eq:app-free-streamline-jet-q0 ¶
    - proves proof app:A-long-proofs@proof-455 ¶
  - depends_on proposition 8.4 Euler's formula ¶
    - depends_on equation 8.2 eq:cpx-exp-series ¶
    - depends_on proposition 7.47 Comparison; absolute convergence ¶ ↺
    - proves proof ch:06-complex-analysis@proof-2 ¶
  - proves proof app:A-long-proofs@proof-456 ¶
- depends_on lemma A.787 From the potential strip to the half plane ¶
  - depends_on definition 8.3 Exponential, sine, cosine ¶ ↺
  - depends_on equation A.1329 eq:app-free-streamline-jet-flux ¶
  - depends_on lemma A.786 From the half-strip to the half plane ¶ ↺
  - proves proof app:A-long-proofs@proof-457 ¶
- depends_on theorem A.783 Riemann mapping with boundary correspondence, quoted ¶
  - depends_on definition 8.5 Complex derivative ¶
  - depends_on theorem 8.6 Cauchy–Riemann equations ¶
    - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on equation 8.4 eq:cpx-derivative ¶
    - proves proof ch:06-complex-analysis@proof-3 ¶
depends_on equation A.1334 eq:app-free-streamline-jet-alpha ¶
depends_on equation A.1329 eq:app-free-streamline-jet-flux ¶ ↺
proves proof app:A-long-proofs@proof-458 ¶

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type	direction	node	provenance	where
`depends_on`	→	The two parameters are the same parameter	declared	appendices/A-long-proofs.tex:38726
`depends_on`	→	eq:app-free-streamline-jet-alpha	declared	appendices/A-long-proofs.tex:38726
`depends_on`	→	eq:app-free-streamline-jet-flux	declared	appendices/A-long-proofs.tex:38726
`proves`	←	app:A-long-proofs@proof-458	declared	appendices/A-long-proofs.tex:38730