Monotonicity properties of some Dini functions
  In this note our aim is to deduce some new monotonicity properties for a special combination of Bessel functions of the first kind by using a recently developed Mittag-Leffler expansion for the derivative of a normalized Bessel function of the first kind. These monotonicity properties are used to obtain some new inequalities for Bessel functions of the first kind. 
\'Arp\'ad Baricz, Tibor K. Pog\'any, R\'obert Sz\'asz
math.CA