Unicity on Entire Function Concerning Its Differential-Difference Operators

摘要

Abstract In this paper, we study the uniqueness of entire function and its differential-difference operators. We prove the following result: let f be a transcendental entire function of finite order, let ηdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$eta $$end{document} be a non-zero complex number, n≥1,k≥0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$nge 1, kge 0$$end{document} two integers and let a and b be two distinct finite complex numbers. If f and (Δηnf)(k)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(Delta _{eta }^{n}f)^{(k)}$$end{document} share a CM and share b IM, then f≡(Δηnf)(k)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$fequiv (Delta _{eta }^{n}f)^{(k)}$$end{document}.