AN ENTIRE FUNCTION SHARING A POLYNOMIAL WITH LINEAR DIFFERENTIAL POLYNOMIALS

The uniqueness problems on entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results on this topic have been obtained. In this paper, we study an entire function f(z) that shares a nonzero polynomial a(z) with f(1)(z), together with its linear differential polynomials of the form: L = L(f) = a(1)(z)f((1)) (z) + a(2)(z)f((2)) (z) + ... + a(n) (z)f((n)) (z), where the coefficients a(k)(z) (k = 1,2, ... , n) are rational functions and a(n) (z) not equivalent to 0.