## Analytic Function Theory, Volume 2This famous work is a textbook that emphasizes the conceptual and historical continuity of analytic function theory. The second volume broadens from a textbook to a textbook-treatise, covering the ``canonical'' topics (including elliptic functions, entire and meromorphic functions, as well as conformal mapping, etc.) and other topics nearer the expanding frontier of analytic function theory. In the latter category are the chapters on majorization and on functions holomorphic in a half-plane. |

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### Contents

I | 1 |

II | 4 |

III | 9 |

IV | 15 |

V | 21 |

VI | 24 |

VII | 31 |

VIII | 38 |

XXXI | 222 |

XXXII | 229 |

XXXIII | 235 |

XXXIV | 241 |

XXXV | 251 |

XXXVI | 257 |

XXXVII | 264 |

XXXVIII | 268 |

IX | 46 |

X | 54 |

XI | 69 |

XII | 77 |

XIII | 82 |

XIV | 87 |

XV | 93 |

XVI | 99 |

XVII | 105 |

XVIII | 109 |

XIX | 115 |

XX | 124 |

XXI | 130 |

XXII | 138 |

XXIII | 144 |

XXIV | 156 |

XXV | 167 |

XXVI | 182 |

XXVII | 192 |

XXVIII | 201 |

XXIX | 211 |

XXX | 219 |

XXXIX | 274 |

XL | 280 |

XLI | 290 |

XLII | 299 |

XLIII | 309 |

XLIV | 320 |

XLV | 325 |

XLVI | 339 |

XLVII | 346 |

XLVIII | 359 |

XLIX | 370 |

L | 385 |

LI | 393 |

LII | 398 |

LIII | 408 |

LIV | 414 |

LV | 421 |

LVI | 429 |

LVII | 444 |

LVIII | 460 |

LIX | 468 |

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### Common terms and phrases

absolutely convergent algebraic function analytic continuation analytic function asserted boundary bounded branch points coefficients completes the proof conformal mapping constant continuous function convex corresponding curve defined denote differential domain elliptic function entire function equals equation exists finite number fn(z follows formula function F(z given gives harmonic Hence holds holomorphic function implies inequality infinite infinity integral interior interval Lemma lim sup line segment linear mapping function meromorphic function neighborhood normal obtain poles polygon polynomial positive number power series problem properties prove radius of convergence rational function real axis regular elements replace result right member roots satisfies Section sector sequence shows simple closed simply-connected single-valued singular point solution spherically Suppose tends to zero theory transformation uniform convergence uniformly with respect unique unit circle unit disk upper half-plane Verify