Article ID Journal Published Year Pages File Type
4616495 Journal of Mathematical Analysis and Applications 2013 11 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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