We discuss the relationship on the periodicity of a transcendental entire function with its differential polynomials. For example, we obtain that if f is a transcendental entire function, k is a non-negative integer and if (a_nfⁿ + ⋯ + a₁f)^(k) is a periodic function, then f is also a periodic function, where a₁, … a_n (≠ 0) are constants. Our results are related to Yang’s Conjecture on the periodicity of transcendental entire functions.

中文翻译：

---

具有微分多项式的超越全函数的周期性

我们讨论超越整个函数与其微分多项式的周期性关系。例如，我们得到如果f是一个超越整函数，k是一个非负整数，如果 ( a _n f ⁿ + ⋯ + a ₁ f ) ^{( k )}是一个周期函数，那么f也是一个周期函数, 其中a ₁ , … a _n (≠ 0) 是常数。我们的结果与杨超越全函数周期性的猜想有关。