满足函数方程的函数称为最简单的周期函数,其中m是某一正数。若m是函数的周期,则am,其中a是任意自然数,也是函数的周期。周期性的这种形式称为加周期性。还存在有周期性的另一种形式,就是满足函数方程的函数性质。这种(更复杂的)周期性,称为乘周期性。在(1)和(2)的情况下,m应理解为这样的实数:在自变量x的任意值下,x±m和mx均属于函数,f(x)的定义域内。函数 The function that satisfies the function equation is called the simplest periodic function, where m is a positive number. If m is the period of the function, then am, where a is an arbitrary natural number, is also the period of the function. This form of periodicity is called cyclical. There is another form of periodicity that satisfies the functional properties of functional equations. This (more complex) periodicity is called periodicity. In the case of (1) and (2), m should be understood as a real number: x m m and mx belong to the function, f(x), within the domain of the definition of an arbitrary value of the variable x. function