q-Extensions of Clausen's formula and of the inequalities used by DeBranges in his proof of the Bieberbach, Robertson and Milin Conjectures
Author: George Gasper
Abstract:
A $q$-extension of the terminating form of Clausen's $\tf$ series
representation for the square of a $\twof(a,b; a+b+1/2; z)$ series is
derived. It is used to prove the nonnegativity of certain basic
hypergeometric series and to derive $q$-extensions of the inequalities
and differential equations de Branges used in his proof of the
Bieberbach, Robertson, and Milin conjectures.
This article published in
SIAM. J. Math. Anal. 20 (1989), 1019--1034.
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