On factorization of a certain class of entire functions (Q1825986)

The authors discuss the primality of the class of entire functions of the form \[ (1)\quad F(z)=Q(z)e^{P(z)}\prod^{N}_{j=1}(e^ z-a_ j)^{\ell_ j}, \] where Q(z), P(z) are polynomials, \[ Q(z)=B_ 0\prod^{K}_{k=1}(z-B_ k)^{h_ k}\not\equiv 0, \] \(B_ 0,B_ 1,...,B_ k\) are distinct constants, \(h_ 1,h_ 2,...,h_ k\), \(\ell_ 1,\ell_ 2,...,\ell_ N\) are integers, \(h_ k\geq 1\) \((k=1,...,K)\), \(\ell_ j\) \((j=1,...,N)\), and \(a_ 1,...,a_ N\) are distinct constants with \(\prod^{N}_{j=1}a_ j\neq 0\). A typical result of the authors is Theorem 1. Then F(z) in (1) is pseudo-prime.