### Certain coefficient andFejerGap series about of homogeneous and non-homogeneous

#### Abstract

To: NevanlinnaTheory in complex differential equation field in has widely of Application, which use the theory research complex linear differential equation meromorphic solution of growth and value distribution and coefficient of growth between the relationship is complex differential equation in the field of important topic. due to incomplete series has some special properties when gap series as an equation coefficient when these properties can be play role. so we can be combined with GAP series of definition and properties research complex linear differential equation meromorphic solution of properties. in this paper in we useNevanlinnaTheory and combinedFej 'ErGap series of definition and properties of a class of homogeneous and non-homogeneous high-order complex linear differential equation the research. When equation of a coefficient andFej 'ErGap series about and the rest of the coefficient for the entire function or meromorphic function when get the equation meromorphic solution of growth level of estimation promotion and improved the previous studies have been results.

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