Radii of convexity of some Lommel and Struve functions

The radii of convexity of some Lommel and Struve functions of the first kind are determined. For both of Lommel and Struve functions three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane. Some results on the zeros of the derivatives of some Lommel and Struve functions of the first kind are also deduced, which may be of independent interest.