【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。更多还原

【Abstract】 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更多还原