Abstract
Our purpose in the present investigation is to study certain geometric properties such as the close-to-convexity, convexity, and starlikeness of the hypergeometric function z{}_{1}F_{2}(a;b,c;z) in the open unit disk. The usefulness of the main results for some familiar special functions like the modified Sturve function, the modified Lommel function, the modified Bessel function, and the {}_{0}F_{1}(-;c;z) function are also mentioned. We further consider a boundedness property of the function _{1}F_{2}(a;b,c;z) in the Hardy space of analytic functions. Several corollaries and special cases of the main results are also pointed out.
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