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Slowly varying functions in the complex plane
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