The Primality of an Entire Function and its Derivative

Abstract:

      In this paper, we deal with the factorization of entire functions in the sense of composition, and prove the following.Theorem. For any real number ρ≥1, there exists a transcendental entire function F(z) of order p , such that there are infinitely many prime elements and infinitely many composite elements in the class {F⁽ⁿ⁾ n = 0.1, 2, …}.