Continuous ranking of zeros of special functions

We reexamine and continue the work of J. Vosmansky [J. Vosmanský, Zeros of solutions of linear differential equations as continuous functions of the parameter k, in: J. Wiener, J.K. Hale (Eds.), Partial Differential Equations, Proceedings of Conference, Edinburg, TX, 1991, in: Pitman Res. Notes Math. Ser., vol. 273, 1992, pp. 253–257] on the concept of continuous ranking of zeros of certain special functions from the point of view of the transformation theory of second-order linear differential equations. This leads to results on higher monotonicity of such zeros with respect to the rank and to the evaluation of some definite integrals. The applications are to Airy, Bessel and Hermite functions.