Slowly varying functions in the complex plane

Monique Vuilleumier
1976 Transactions of the American Mathematical Society  
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 -* •».
doi:10.1090/s0002-9947-1976-0399479-4 fatcat:dqpsjwqpd5evjgqixai3iwonky