Properties And Applications Of Meromorphic Functions With Finite Logarithmic Growth Order

In this paper,the properties and applications of meromorphic functions with finite logarithmic growth levels are studied.First,the properties of some function product and sum logarithmic growth levels of the meromorphic functions with finite logarithmic growth levels are studied.Next,the property of the finite logarithmic growth level mero-morphic function and q-difference form Wiman-Valiron theory obtain the relationship between the meromorhic solution and the coefficient of linear difference equationThe full text is organized as followsIn Chapter 2,we introduce Nevanlinna theory,difference Nevanlinna theoryIn Chapter 3,we introduce q-difference equation,q-difference Nevanlinna theoryIn Chapter 4,we introduce properties and applications of meromorphic functions with finite logarithmic growth orderThe main results of this paper areTheorem 1.Let f(z)and g(z)are nonconstant meromorphic functions on the complex plane and their logarithmic growth orders are ?log(f)and ?log(g).?log(fg)?max{?log(f),?log(g)},?log(f+g)?max{?log(f),?log(g)},that is,the logarithmic growth order of produce and sum of two meromorphic functions is not greater than that of the larger logarithmic growth order of two meromorphic functions.Theorem 2.Let f(z)and g(z)are nonconstant meromorphic functions on the complex plane and the logarithmic growth order of f(z)is ?log(f)and the lower level of logarithmic growth order is ?log(g),if plog(?)<?log(g),then T(r,?)= o(T(r,g))(r??).Theorem 3.Let a0(z),...,an(z)are transcendental integral function with finite logarithmic growth order,and let q ? C\{0} to |q|?1.For the following euqation f(z)is the transcendental integral solution of the equation,and there exists i ?{0,...,n}and then...