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On the order of starlikeness of hypergeometric functions. (English) Zbl 0598.30021
An analytic function f in a domain D is called starlike of order $\gamma <1$ if and only if $$ f(0)=0,\quad f'(0)=1\quad and\quad Re[zf'(z)/f(z)]>\gamma,\quad z\in D. $$ $S\sp*\sb{\gamma}$ denotes the set of these functions. The authors estimate the order of starlikeness of the hypergeometric functions $u(z)=z\sb 2F\sb 1(a,b;c: \rho z)$. Some interesting applications and a confluent case have also been given.
Reviewer: A.D.Wadhwa

30C45Special classes of univalent and multivalent functions
33C05Classical hypergeometric functions, ${}_2F_1$
Full Text: DOI
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