Ultraholomorphic

Under this assumption, and through the characterization of strongly regular sequences in terms of so-called regular variation, we show that the growth index #92;gamma(#92;mathbb#123;M#125;) defined by V.Thilliez (Division by flat ultradifferentiable functions and sectorial extensions, Results Math. 44 (2003), 169--188) and the order of quasianalyticity #92;omega(#92;mathbb#123;M#125;) introduced by the second author (Flat functions in Carleman ultraholomorphic classes via proximate orders, J.