第一类切比雪夫型基本方程的重根规律

The Multiple Root Laws of the First Kind Tschebyscheff Basic Equation

探讨了第一类切比雪夫型基本方程Tn(x)=Tm(x)的重根现象,得到Tn(x)=Tm(x)有重根的充要条件、其全体复根均为单根的充要条件和计算重根个数的公式这三个定理以及一些有用的推论.

This paper studies the multiple root phenomenon of the first kind Tschebyscheff basic equation Tn（x）=Tm（x） and gets three theorems ：the necessary and sufficient condition of having multiple root of Tn（x）=Tm（x） ,the necessary and sufficient condition of only having single root of Tn（x）=Tm（x） as well as the expression on counting the number of its multiple root. Besides, it also gets some other useful conclusions.