Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives

In this paper, we investigate the uniqueness problem of entire functions sharing two polynomials with their k-th derivatives. We look into the conjecture given by Lu, Li and Yang [Bull. Korean Math. Soc., 51 (2014), 1281-1289] for the case F = f(n) P(f), where f is a transcendental entire function and P(z) = a(m)z(m) + a(m-1)z(m-1) + . . . + a(1)z + a(0) (not equivalent to 0), m is a nonnegative integer, a(m), a(m-1), ... ,a(1), a(0) are complex constants and obtain a re sult which improves and generalizes many previous results. We also provide some examples to show that the conditions taken in our result are best possible.