CAJ | 학술논문

深入研究并分析切比雪夫序列的短周期现象,并通过数学证明,对于任意整数阶切比雪夫序列,在初值角度取有限小数时必会退化为短周期序列. 首先,通过证明得到切比雪夫序列退化为短周期序列的等价条件;然后,利用分类讨论的思想证明任意整数阶切比雪夫序列在初值角度取整数时,必会退化为短周期序列;最后,通过数学归纳法将这一结论扩展到任意有限精度初值上,得出切比雪夫序列在初值精度有限时退化为周期序列.
심입연구병분석절비설부서렬적단주기현상,병통과수학증명,대우임의정수계절비설부서렬,재초치각도취유한소수시필회퇴화위단주기서렬. 수선,통과증명득도절비설부서렬퇴화위단주기서렬적등개조건;연후,이용분류토론적사상증명임의정수계절비설부서렬재초치각도취정수시,필회퇴화위단주기서렬;최후,통과수학귀납법장저일결론확전도임의유한정도초치상,득출절비설부서렬재초치정도유한시퇴화위주기서렬.
The short-period problems of Chebyshev sequences had been researched, and aconclusion that Chebyshev sequences of random integer order will degenerateinto short-period sequences while Chebyshev equivalent conditions about Chebyshevsequences degenerating into short-period sequences had been shown first, andthen an integer order Chebyshev sequences whose initial value is integermust degenerate into short-period sequence has been proved. Finally, theinitial value conditions has been extended to finite decimal by usingmathematical induction method.