Real meromorphic functions and linear differential polynomials

Abstract

We determine all real meromorphic functions f in the plane such that f has finitely many zeros, the poles of f have bounded multiplicities, and f and F have finitely many non-real zeros, where F is a linear differential polynomial given by F = f (k) + k−1 j=0 a j f (j) , in which k 2 and the coefficients a j are real numbers with a 0 = 0.