关于车比雪夫多项式卷积的正交性

On the orthogonality of the convolution of Chebyshev polynomials

设Un(x)表示第二类车比雪夫多项式。即U0(x)=1,U1(x)=2x,当n≥1时有递推关系式Un+1(x)=2x Un(x)-Un-1(x)。文中的主要目的是运用初等方法以及幂级数的性质研究Un(x)的一类卷积的正交性问题,并给出该类卷积的一个有趣的积分计算公式。

For any integer n≥0, let Un （x） denotes the second kind Chebyshev polynomicals. That is, U0 （x） = 1 ,U2 （x） =2x, and Un＋1 （x） =2xUn（x） - Un-1 （x） for all positive integer n≥1. The main purpose of this paper is using the elementary method and the properties of power series to study the computational problem of the convolution involving the second kind Chebyshev polynomials, and give an interesting computational formula for it.