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
\[
f(0)=0,\quad f'(0)=1\quad and\quad Re[zf'(z)/f(z)]>\gamma,\quad z\in D.
\]
\(S^*_{\gamma}\) denotes the set of these functions. The authors estimate the order of starlikeness of the hypergeometric functions \(u(z)=z_ 2F_ 1(a,b;c: \rho z)\). Some interesting applications and a confluent case have also been given.
Reviewer: A.D.Wadhwa
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
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