Slowly Varying Functions in the Complex Plane

  • MONIQUE VUILLEUMIER
  • Published 2010

Abstract

Let /be analytic and have no zeros in lar« z\ < a < tr, /is called slowly varying if, for every \ > 0,/(az)//(z) -» 1 uniformly in larg z| < ß < a, when Iz I -* ». One shows that / is slowly varying if and only if z/'(z)//(z) ■+ 0 uniformly in larg z\ < ß < a, when Izl -* •».