On properties of meromorphic solutions for difference equations concerning gamma function

In this paper, we mainly consider the properties of differences of meromorphic solutions for the difference equation a 1 ( z ) f ( z + 1 ) + a 0 ( z ) f ( z ) = 0 concerning a Gamma function, where a 1 ( z ) and a 0 ( z ) are nonzero polynomials. By these properties, we deduce that a Gamma function satisfies that for every n ∈ N , λ ( Δ n Γ ( z ) ) = λ ( Γ ( z ) ) = 0 , Δ n Γ ( z ) has only n zeros , τ ( Γ ( z ) ) = τ ( Δ Γ ( z ) ) = τ ( Γ ( z + j ) ) = σ ( Γ ( z ) ) = 1 ( j = 0 , 1 , … ) , λ ( Δ n 1 Γ ( z ) ) = λ ( 1 Γ ( z ) ) = 1 , Δ n 1 Γ ( z ) and 1 Γ ( z ) have same zeros, at most except n exceptional zeros, where σ ( g ) denotes the order of growth of a meromorphic function g , and τ ( g ) and λ ( g ) denote the exponents of convergence of fixed points and zeros of g respectively.