On the Regular Variation of Main Characteristics of an Entire Function - Filevych, P. V.; Sheremeta, M. M. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
We establish a necessary and sufficient condition for the coefficients a n of an entire function \(f(z) = \sum {_{n = 0}^∞ } {\text{ }}a_n z^n \) under which its central index and the logarithms of the maximum of the modulus and the maximum term are regularly varying functions. We construct an entire function the logarithm of the maximum of whose modulus is a regularly varying function, whereas the Nevanlinna characteristic function is not a regularly varying function.