Uniqueness of entire functions with its derivative (Q2712483)

The author improves and generalizes further the theorem of L. A. Rubel and C. C. Yang, obtains two theorems and two corollaries for the uniqueness of entire functions that share two pairs of small functions CM with their derivatives. For example: Let \(f\) be a non-constant entire function. If \(f\) and \(f^{(k)}\) share a pair of small functions \(a,b\) CM, where \(k\) is a positive integer and \(a\neq b,a,b\not \equiv\infty\), then \(f\equiv f^{(k)}\).