Composition of entire functions with finite iterated order

In this paper, we investigate the growth of two composite entire functions of finite iterated order and a series of comparative growths of log p + q T ( r , f ( g ) ) ( p , q ∈ N ) with log p T ( r , f ) and log q T ( r , g ) . At the end of this paper, we apply some growth results into the factorization of the solutions of linear differential equation. We achieve some results which are the improvements and extensions of the previous results.