定理8＇函数f(x)是非负的周期函数,若n为正偶数, 则函数[f(x)]是周期函数,且函数[f(x)]与f(x)的周期一致.
3.2.4.3
1n1nn为负奇数时,函数[f(x)]的定义域与
1n1的定义域相同,且f(x)11?{[f(x)]n}?n. f(x)因此,由定理9,有
定理9＇函数f(x)是不恒为零的周期函数,若n为负奇数，则函数[f(x)]是周期函数,且函数[f(x)]与
3.2.4.4
1n1n1的周期一致. f(x)1nn为负偶数时,函数f(x)是不恒为零的非负的周期函数, 函数[f(x)]的定义
111域与的定义域相同,且{[f(x)]n}?n?.
f(x)f(x)因此,由定理10,有
定理10＇函数f(x)是不恒为零的非负的周期函数,若n为负偶数，则函数[f(x)]是周
11期函数,且函数与[f(x)]n的周期一致.
f(x)1n
参考文献
[1]王清印,吴和琴.函数周期性初论[M].北京:煤炭工业出版社,1987.
[2]梁力平.对周期函数及其和、差、积、商函数周期性的探讨[J]. 韶关学院学报,2006,(27).
[3]杨曼英.关于周期函数及最小正周期的探讨[J]. 娄底师专学报,2001,(2). [4]费强.周期函数性质初探[J].数学学习与研究,2014,(13). [5]宣立新,马明.周期函数初论[M].合肥:安徽教育出版社,1989.
[6]潘劲松.关于周期函数定义的研究[J]. 湖南师范大学自然科学学报,2012,(35).
英文摘要
Probed into cycle function and cycle properties of the sum, the difference, the product and the quotient of it
Abstract The paper probes into the definition of cycle function and cycle,
cycle properties of cycle function and the definition of least positive cycle, and furthermore
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probes into cycle properties of the sum ,the difference ,the product ,the quotient of cycle function ,thus coming to its theorem ,and illustrates its application.
Key words cycle function; cycle; cycle properties; least positive cycle
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周期函数运算（加，减，乘除，复合）结果分析
