We will provide sufficient conditions for the shifted hypergeometric function $z_2F_1(a,b;c;z)$ to be a member of a specific subclass of starlike functions in terms of the complex parameters $a,b$ and $c.$ For example, we study starlikeness of order $alpha,$ $lambda$-spirallikeness of order $alpha$ and strong starlikeness of order $alpha.$ In particular, those properties lead to univalence of the shifted hypergeometric functions on the unit disk.
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