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A short proof of an inequality used by de Branges in his proof of the Bieberbach, Robertson and Milin conjectures. (English) Zbl 0605.30018

The author gives a short proof of an inequality for special hypergeometric series which was the last step in de Branges proof of the Milin conjecture implying that the famous Bieberbach conjecture is true [see: L. de Branges, Acta Math. 154, 137-152 (1985; Zbl 0573.30014)]. Another proof of this inequality involving a lot of theorems on special functions was given before by R. Askey and G. Gasper [Am. J. Math. 98, 709-737 (1976; Zbl 0355.33005)]. Furthermore the author discusses some possible extensions of the Milin conjecture.
Reviewer: K.-J.Wirths

MSC:

30C50 Coefficient problems for univalent and multivalent functions of one complex variable
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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