A short proof of an inequality used by de branges in his proof of the bieberbach, robertson and milin conjectures

1 December 1986

journal article
research article
Published by Taylor & Francis in Complex Variables and Elliptic Equations

Vol. 7 (1) , 45-50
https://doi.org/10.1080/17476938608814185

Abstract

Clausen's formula for the product of two hypergeometric series and a summation formula are used to give a short proof of an inequality used by de Branges in his proof of the Bieberbach, Robertson, and Milin conjectures. Some possible extensions of the de Branges-Milin inequality are pointed out.

Keywords

This publication has 11 references indexed in Scilit:

A proof of the Bieberbach conjecture
Acta Mathematica, 1985
Logarithmic coefficients of univalent functions
Journal d'Analyse Mathématique, 1979
Applications of a Convolution Theorem to Jacobi Polynomials
SIAM Journal on Mathematical Analysis, 1979
Positive Sums of the Classical Orthogonal Polynomials
SIAM Journal on Mathematical Analysis, 1977
Positive Jacobi Polynomial Sums, II
American Journal of Mathematics, 1976
Positivity and Special Functions
Published by Elsevier ,1975
A proof of the Bieberbach conjecture for the fifth coefficient
Archive for Rational Mechanics and Analysis, 1972
An elementary proof of the Bieberbach conjecture for the sixth coefficient
Kodai Mathematical Journal, 1969
A proof of the Bieberbach conjecture for the sixth coefficient
Archive for Rational Mechanics and Analysis, 1968
Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I
Mathematische Annalen, 1923