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

Abstract

Given an unbounded non-decreasing positive function φ, we studied what the relations are between the growth order of any solution of a complex linear differential–difference equation whose coefficients are entire or meromorphic functions of finite φ-order. Our findings extend some earlier well-known results.

Keywords

• Nevanlinna
• complex solution
• growth order
• complex linear ODE