Abstract
In this note, we will continue the previous consideration concerning the factorization (under composition) of entire functions belonging to the class J(2πi)(consisting of entire functions of the form: z + H(z), where H(z + πi)= H(z) is entire) and prove some results on the unique factorizability and the primeness for certain kinds of such entire functions. For the proof we shall make use of Theorems due to Bergweiler as well as Steinmetz, together with some, already known, fundamental facts.
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