The periodicity on a transcendental entire function with its
differential-difference polynomials
Yong Liua,b,*, Shuai Jianga
ABSTRACT: According to a conjecture by C. C. Yang [Houston J Math 45 (2019):431?437], if ?(z)?(k)
(z) is a periodic
function, where ?(z) is a transcendental entire function and k is a positive integer, then ?(z) is also a periodic function.
We consider the related questions, which can be viewed as differential-difference versions of Yang?s conjecture. We
discuss the periodicity of a transcendental entire function ?(z) when differential-difference polynomials in ?(z) are
periodic.