Classical Topics in Complex Function Theory

Preface 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 i [...]
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Preface 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."