engleski

Starlikeness of a cross-product of Bessel functions

In this paper a necessary and sufficient condition is deduced for the close-to-convexity of a cross- product of Bessel and modifi ed Bessel functions of the fi rst kind and their derivatives by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives, the newly discovered power series and in finite product representation of this cross-product, as well as a slightly modi fied version of a result of Lorch on the monotonicity of the zeros of the cross-product with respect to the order.

Bessel functions of the fi rst kind; Modifi ed Bessel functions of the fi rst kind; Close-to-convex functions; Starlike functions; Transcendental entire functions; Zeros of cross-product of Bessel functions; Infi nite product.

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