关于切比雪夫递推方程组的若干研究

Study on Tschebyscheff Recursive Equations

应用第一类切比雪夫多项式的递推关系及初始值定义了第一类二元一阶切比雪夫递推方程组和多元一阶切比雪夫递推方程组,运用代数变换法和归纳演绎法得到各数列的通项公式,研究了第一类多元一阶切比雪夫递推方程组通项公式的结构及规律.

The recurrence relation and initial values of the first Tschebyscheff polynomials are employed to define the binary first-order and multivariate first-order Tschebyscheff recursive equations. Using the methods of algebraic transformation, induction and deduction, the general formula of series is achieved. The structures of general formula of the first multivariate first-order Tschebyscheff reeursive equations are studied.