## 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.

### MSC:

 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 33C05 Classical hypergeometric functions, $${}_2F_1$$

### Keywords:

order of starlikeness; hypergeometric functions; confluent
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### References:

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