## Classical Topics in Complex Function Theory, Volume 172Preface to the Second German Edition In addition to the correction of typographical errors, the text has been materially changed in three places. The derivation of Stirling's formula in Chapter 2, §4, now follows the method of Stieltjes in a more systematic way. The proof of Picard's little theorem in Chapter 10, §2, is carried out following an idea of H. Konig. Finally, in Chapter 11, §4, an inaccuracy has been corrected in the proof of Szego's theorem. Oberwolfach, 3 October 1994 Reinhold Remmert Preface to the First German Edition Wer sich mit einer Wissenschaft bekannt machen will, darf nicht nur nach den reifen Friichten greifen - er muB sich darum bekiimmern, wie und wo sie gewachsen sind. (Whoever wants to get to know a science shouldn't just grab the ripe fruit - he must also pay attention to how and where it grew. ) - J. C. Poggendorf Presentation of function theory with vigorous connections to historical de velopment and related disciplines: This is also the leitmotif of this second volume. It is intended that the reader experience function theory personally viii Preface to the First German Edition and participate in the work of the creative mathematician. Of course, the scaffolding used to build cathedrals cannot always be erected afterwards; but a textbook need not follow Gauss, who said that once a good building l is completed its scaffolding should no longer be seen. Sometimes even the framework of a smoothly plastered house should be exposed. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

V | 3 |

VI | 4 |

VII | 6 |

VIII | 7 |

X | 9 |

XI | 10 |

XII | 12 |

XIV | 14 |

CLVIII | 171 |

CLIX | 172 |

CLX | 174 |

CLXI | 175 |

CLXIII | 177 |

CLXV | 178 |

CLXVI | 179 |

CLXVII | 180 |

XV | 15 |

XVI | 16 |

XVII | 17 |

XVIII | 18 |

XIX | 19 |

XX | 20 |

XXI | 22 |

XXII | 24 |

XXIII | 25 |

XXV | 26 |

XXVI | 28 |

XXVII | 30 |

XXVIII | 33 |

XXIX | 36 |

XXXI | 37 |

XXXII | 39 |

XXXIV | 41 |

XXXV | 42 |

XXXVI | 43 |

XXXVII | 45 |

XXXVIII | 46 |

XXXIX | 47 |

XL | 49 |

XLI | 51 |

XLII | 52 |

XLIII | 53 |

XLIV | 55 |

XLV | 56 |

XLVI | 58 |

XLVII | 59 |

XLVIII | 60 |

XLIX | 61 |

L | 63 |

LI | 64 |

LII | 66 |

LIII | 67 |

LIV | 68 |

LV | 69 |

LVI | 70 |

LVII | 73 |

LVIII | 74 |

LX | 75 |

LXI | 76 |

LXII | 77 |

LXIII | 78 |

LXIV | 79 |

LXV | 80 |

LXVI | 81 |

LXVII | 82 |

LXVIII | 83 |

LXIX | 85 |

LXXI | 86 |

LXXII | 89 |

LXXIII | 90 |

LXXIV | 91 |

LXXV | 92 |

LXXVII | 93 |

LXXVIII | 94 |

LXXX | 96 |

LXXXI | 97 |

LXXXIII | 99 |

LXXXIV | 100 |

LXXXVI | 102 |

LXXXVIII | 104 |

LXXXIX | 107 |

XCI | 108 |

XCII | 109 |

XCIV | 110 |

XCV | 111 |

XCVI | 112 |

XCVII | 113 |

XCVIII | 115 |

XCIX | 116 |

C | 118 |

CI | 119 |

CII | 120 |

CV | 122 |

CVII | 123 |

CVIII | 125 |

CIX | 126 |

CXI | 127 |

CXII | 128 |

CXIV | 129 |

CXV | 130 |

CXVI | 131 |

CXVIII | 132 |

CXIX | 133 |

CXX | 134 |

CXXI | 135 |

CXXII | 136 |

CXXIV | 138 |

CXXVI | 139 |

CXXVII | 140 |

CXXVIII | 141 |

CXXIX | 142 |

CXXX | 145 |

CXXXI | 147 |

CXXXII | 148 |

CXXXIV | 150 |

CXXXVII | 151 |

CXXXVIII | 152 |

CXL | 153 |

CXLI | 154 |

CXLIII | 156 |

CXLV | 157 |

CXLVI | 158 |

CXLVII | 159 |

CXLIX | 160 |

CL | 161 |

CLI | 162 |

CLII | 164 |

CLIII | 167 |

CLIV | 168 |

CLVI | 169 |

CLVII | 170 |

CLXVIII | 181 |

CLXX | 183 |

CLXXI | 184 |

CLXXIII | 186 |

CLXXIV | 187 |

CLXXV | 188 |

CLXXVII | 189 |

CLXXIX | 191 |

CLXXXII | 192 |

CLXXXIII | 193 |

CLXXXIV | 194 |

CLXXXVI | 195 |

CLXXXVII | 196 |

CLXXXVIII | 197 |

CLXXXIX | 198 |

CXC | 199 |

CXCI | 201 |

CXCII | 203 |

CXCIII | 204 |

CXCV | 205 |

CXCVI | 206 |

CXCVIII | 207 |

CC | 208 |

CCI | 209 |

CCII | 210 |

CCIII | 211 |

CCIV | 212 |

CCVI | 213 |

CCVII | 215 |

CCVIII | 216 |

CCIX | 217 |

CCXI | 218 |

CCXII | 219 |

CCXIII | 220 |

CCXIV | 221 |

CCXVI | 223 |

CCXVII | 225 |

CCXVIII | 226 |

CCXX | 227 |

CCXXI | 228 |

CCXXII | 230 |

CCXXIII | 232 |

CCXXIV | 233 |

CCXXVI | 234 |

CCXXVII | 235 |

CCXXVIII | 236 |

CCXXIX | 237 |

CCXXX | 238 |

CCXXXI | 239 |

CCXXXII | 240 |

CCXXXV | 241 |

CCXXXVI | 243 |

CCXXXVII | 244 |

CCXXXIX | 245 |

CCXL | 247 |

CCXLI | 248 |

CCXLII | 249 |

CCXLV | 250 |

CCXLVI | 252 |

CCXLVII | 253 |

CCXLVIII | 254 |

CCXLIX | 255 |

CCLI | 256 |

CCLII | 257 |

CCLIII | 258 |

CCLIV | 259 |

CCLVI | 260 |

CCLVIII | 262 |

CCLIX | 263 |

CCLXI | 265 |

266 | |

CCLXIII | 267 |

CCLXIV | 268 |

CCLXV | 269 |

CCLXVI | 271 |

CCLXVII | 272 |

CCLXVIII | 273 |

CCLXX | 275 |

CCLXXI | 276 |

CCLXXII | 278 |

CCLXXIV | 281 |

CCLXXV | 283 |

CCLXXVI | 284 |

CCLXXVII | 287 |

CCLXXIX | 289 |

CCLXXX | 290 |

CCLXXXI | 291 |

CCLXXXII | 292 |

CCLXXXIV | 293 |

CCLXXXV | 294 |

CCLXXXVI | 295 |

CCLXXXVIII | 296 |

CCLXXXIX | 297 |

CCXC | 298 |

CCXCI | 299 |

CCXCII | 300 |

CCXCIV | 302 |

CCXCV | 303 |

CCXCVII | 304 |

CCXCVIII | 305 |

CCC | 306 |

CCCI | 309 |

CCCII | 310 |

CCCIII | 311 |

CCCIV | 312 |

CCCV | 313 |

CCCVII | 314 |

CCCVIII | 315 |

CCCIX | 316 |

CCCX | 318 |

CCCXII | 321 |

CCCXIII | 329 |

331 | |

337 | |

### Common terms and phrases

Algebraic approximated uniformly arbitrary biholomorphic boundary point called Caratheodory Cauchy closed path coefficients compact set compactly in G constant construction converges compactly converges normally Corollary denote domain G domain of holomorphy entire function equation Euler example existence theorem expansion follows immediately formula function f function holomorphic function theory Funktionen hence holds holes holomorphic functions ideal integral Journ Koebe domain lemma Let f Let G locally bounded locally finite logarithmic Math mathematician meromorphic functions Mittag-Leffler series Mittag-Leffler's theorem Montel Montel's theorem neighborhood nonconstant nonvanishing normal convergence null homologous Picard's little theorem pointwise poles polynomial positive divisor power series principal part distribution product theorem Proof Proposition prove radius region Riemann mapping theorem Runge pair Runge's Section simply connected simply connected domains Springer statement Stein Subsection Taylor series topological Uber uniqueness theorem Vitali's theorem Weierstrass product Werke zero