Value distribution of certain type of difference polynomials (Q1723744)

Summary: We investigate the value distribution of difference product \(f(z)^n \sum_{i = 1}^k a_i f(z + c_i)\), for \(n \geq 2\) and \(n = 1\), respectively, where \(f(z)\) is a transcendental entire function of finite order and \( a_i\), \(c_i\) are constants satisfying \(\sum_{i = 1}^k a_i f(z + c_i) \not\equiv 0\).