HIGHER MONOTONICITY PROPERTIES AND INEQUALITIES FOR ZEROS OF BESSEL-FUNCTIONS

L. Lorch and P. Szego have considered the sign-regularity of the higher differences (with respect to the rank k) of the sequence {C(vk)} of positive zeros of the Bessel function C(v)(x). Our main purpose here is to extend one of their main results to the higher derivatives with respect to kappa when C(vk) is appropriately defined as a function of a continuous variable kappa rather than the discrete variable kappa, and the difference operator is replaced by a derivative operator. We also present some inequalities arising from these and other results.