New properties of the generalized Dini function. (English) Zbl 1488.33061
Summary: In this work we study some properties of the normalized form of generalized Dini function like close-to-convexity of some order and close-to-convex with respect to another convex function. Furthermore, we investigate sufficient conditions which these functions are uniformly \(k\)-starlike functions of complex order \(b\) in the open unit disk, and some consequences of the main results are also presented.
MSC:
| 33E12 | Mittag-Leffler functions and generalizations |
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
Keywords:
analytic functions; univalent function; Bessel functions of first kind of order \(\nu\); modified Dini function; starlike; convex and close-to-convex functions of order \(\alpha\)References:
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