The factorization theorems of analytic functions with finitely or infinitely many zeros in the unit disc

In this paper, we make use of the complex function u=(R Z k /|Z k |-Z k )/(R Z k /|Z k |-Z) and prove the factorization theorems of analytic functions with finitely or infinitely many zeros in the disc D R = {z∈C :| z |<; R <; ∞}, where C is the complex plane.