We use the theory of normal families to prove the following. Let and be two polynomials such that (where is a nonnegative integer) and are two distinct complex numbers. Let be a transcendental entire function. If and share the polynomial and if whenever , then . This result improves a result due to Li and Yi.
"Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives." Abstr. Appl. Anal. 2009 1 - 9, 2009. https://doi.org/10.1155/2009/847690