ultraholomorphic

ultra- +‎ holomorphic

ultraholomorphic (not comparable)

1. (mathematics) Holomorphic and such that all derivatives are uniformly bounded by a constant multiple of the argument that can be associated with the order of the derivative.
   • 2015, Javier Jiménez-Garrido, Javier Sanz, “Strongly regular sequences and proximate orders”, in arXiv‎:

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