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arXiv · 1410.6266

Starlikeness of a cross-product of Bessel functions

Huda A. Al-Kharsani·Árpád Baricz·Tibor K. Pogány
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Abstract

In this paper a necessary and sufficient condition is deduced for the close-to-convexity of a cross product of Bessel and modified Bessel functions of the first 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 infinite product representation of this cross-product, as well as a slightly modified version of a result of Lorch on the monotonicity of the zeros of the cross product with respect to the order.

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Huda A. Al-Kharsani, Árpád Baricz, Tibor K. Pogány. 2014-10-23. Starlikeness of a cross-product of Bessel functions. https://arxiv.org/abs/1410.6266

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