对周期函数的一些探讨

Discussions on Periodic Function

通常对周期函数是这样定义的，设f（x）是定义在某一数集M上的函数、若存在一常数T（T≠0）具有x＋T，x∈M，f（x＋T）=f（x），那么称f（x）为集M上的周期函数。实际上有周期性规律的函数，并非这一种情况，还有其它多种情形，如乘性规律的、迭代性规律的等。本文将对各种有周期性规律的函数给以科学的概括，并加以推广。

Periodic Function is usually defined as follows, suppose, f（x） is a function defined at a certain number called M, and there is a constant T（T ≠0） with x ＋ T, x ∈ M, f（x ＋ T）=f（x）, f（x） is named as a periodic function at the number M. In fact, periodic function does not exist in this ease alone. Instead, there are many of them such as multiplying function and hierarchical function etc. This paper will generalize periodic function and its extension.