On the Iterated Exponent of Convergence of Solutions of Linear Differential Equations with Entire and Meromorphic Coefficients

Abstract

We investigate the zeros of the difference of the derivative of solutions of the higher-order linear differential equationsf(k)+Ak-1(z)f(k-1)+⋯+A1(z)f′+A0(z)f=0and small functions, whereA0(z),…,Ak-1(z)are entire or meromorphic functions of finite iteratedporder.

Picturing the Growth Order of Solutions in Complex Linear Differential–Difference Equations with Coefficients of φ-Order

“…Finally, let us recall that Chyzhykov et al [30] considered the concept of the ϕ-order of a function f , meromorphic in the unit disc, where ϕ : [0, ∞) → (0, ∞) is an unbounded non-decreasing real function. Later on, this concept was revisited by Shen et al [31] and Bouabdelli/Belaidi [32], who extended it and, additionally, explicated the corresponding ϕ-lower-order definitions that we recall in the following section.…”