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 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. 
Huda A. Al-Kharsani, \'Arp\'ad Baricz, Tibor K. Pog\'any
math.CA