A generalization of the Lindelöf theorem

Abstract

We present a generalization of the Lindelöf theorem on conditions that should be imposed on the coefficients of the Taylor series of an entire transcendental function ƒ in order that the relation $ln M_f (r) - \tau r^\rho , r \to \infty , M_f (r) = \max \left\{ {\left| {f(r)} \right|:|z| = r} \right\}$ , be satisfied.