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Zbl 0598.30021
Ruscheweyh, St.; Singh, V.
On the order of starlikeness of hypergeometric functions. (English)
[J] J. Math. Anal. Appl. 113, 1-11 (1986). ISSN 0022-247X

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.
[A.D.Wadhwa]

MSC 2000:: *30C45 Special classes of univalent and multivalent functions
33C05 Classical hypergeometric functions

Keywords: order of starlikeness; hypergeometric functions; confluent

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