On the order of starlikeness of hypergeometric functions (Q1079690)

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.