On the Asymptotic Properties of Functions of Finite Order, Analytic in a Disk, Represented by Series in Systems of Functions

In terms of order, lower order, type, lower type and two-member power asymptotic for the function A(z)=∑n=1∞anf(λnz), analytic in a finite disk, where f is an entire transcendental function and (λn) is sequence of positive numbers increasing to +∞, the relationship between the growth of M(r,A)=∑n=1∞|an|Mf(rλn), where Mf(r)=max{|f(z)|:|z|=r}, and the behavior of the coefficients an, is studied.