Generalization of the Lindelöf Theorem to the Case of Boutroux Proximate Order

Generalization of the Lindelöf Theorem to the Case of Boutroux Proximate Order. II

“…We note that (1.3) implies p + 1 < α + 1 and p + 2 > ρ + 1. Then from the asymptotic inequality μ f (r) < (Δ f + ε)V (r) and [1]…”

“…This paper continues the study of [1]. An important role in the theory of entire functions is played by theorems establishing a connection between the type of an entire function and the decrease rate of coefficients in a power expansion of this function or distribution of its zeros.…”

“…To estimate the first and second integrals, we use the inequalities (2.1) and (2.2) in [1] respectively. By (2.3),…”

On the Type of Subharmonic Functions of Finite Order

“…We will call an inequality that holds for all sufficiently large values of r the asymptotic inequality. We will use two lemmas from [25].…”