Certain geometric properties of generalized Dini functions
Summary: We are mainly interested in some geometric properties for the combinations of generalized Bessel functions of the first kind and their derivatives known as Dini functions. In particular, we study the starlikeness of order \(\alpha,\) convexity of order \(\alpha\), and close-to-convexity of order \(((1 + \alpha) / 2)\) for normalized Dini function. We also study close-to-convexity with respect to certain star-like functions. Further, we obtain conditions on generalized Dini function to belong to the Hardy space \(\mathcal{H}^p\).
scientific article; zbMATH DE number 6967286
scientific article