摘要
切比雪夫多项式是可以用三角函数简单表示的正交多项式。本文表明,用三角函数的形式,可以定义另外两类正交多项式V_n(x)=(cos(n+1/2)~θ)/cosθ/2 cosθ=xW_n(x)=(sin(n+1/2)~θ)/(cosθ/2) cosθ=x这两类新的多项式的正交性和其他性质,以及它们与第一类和第二类切比雪夫多项式之间的关系,在文中均加以讨论。
The Tchebycheff polynomials of the first and second kinds are orthognal polyno- mials which may be represented simply by trigonometric functions.It is shown in thsi paper that two new kinds of orthogonal polynomials can be represented by trigonome- tric functions too.They are V_n(x) =cos(n+θ/2)/cos θ/2 cosθ=x W_n(x) =sin(n+1/2)θ/sin θ/2 cosθ=x The orthogonality and other properties of these polynomials as well as their relation with the Tchebycheff polynomialas of the first and the second kinds are discussed
关键词
多项式
切比雪夫
正交多项式
orthogonal polynomials
Tchebycheff polynomials
