thank you advance sir

Problem 4. Suppose that f E H (C) and f(n) = 0 for all n E Z. Show that all the singularities of f(z)/ 5111(11-2) are removable. Problem 5. Suppose that f E H((C), f(z+ 1) = if(z) for all z, f(0) = 0, and |f(z)| S ewllmzl for all 2. Show that f (z) = csin(7rz) for some constant c. Notations: