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 a1(z)f(z+1)+a0(z)f(z)=0a1(z)f(z+1)+a0(z)f(z)=0 concerning a Gamma function, where a1(z)a1(z) and a0(z)a0(z) are nonzero polynomials. By these properties, we deduce that a Gamma function satisfies that for every n∈Nn∈N, λ(ΔnΓ(z))=λ(Γ(z))=0,ΔnΓ(z)has onlynzeros ,τ(Γ(z))=τ(ΔΓ(z))=τ(Γ(z+j))=σ(Γ(z))=1(j=0,1,…),λ(Δn1Γ(z))=λ(1Γ(z))=1,Δn1Γ(z) and 1Γ(z) have same zeros, at most except nn exceptional zeros, where σ(g)σ(g) denotes the order of growth of a meromorphic function gg, and τ(g)τ(g) and λ(g)λ(g) denote the exponents of convergence of fixed points and zeros of gg respectively.