关于带有切彼雪夫权函数的高斯型求积公式的一点注记

Remarks on Gauss Type Quadrature Formula with Cheyshev

给出了带有Ｃｈｅｂｙｓｈｅｖ权函数的Ｇｓｕｄｓｓ型求积公式，Ｇａｕｓｓ－Ｌｏｂａｔｔｏ求积公式对于多项式函数ｘ２ｋ＋１，ｋ＝０，１，２，…精确地成立（一般地，求积公式对于连续的奇函数也精确成立），对于带有Ｃｈｅｂｙｓｈｅｖ权函数，具有ｎ＋１个节点的Ｇａｕｓｓ－Ｒａｄａｕ求积公式对于多项式函数ｘ２ｎ＋２精确成立。

This note gives that Gauss quadrature formula and Gauss-Lobatto quadrature formu- la with chebyshev weight function hold exactly for polynomial function x2k+1 , k=0,1…(In gen- eral, quadrature formulas hold exactly also for continuous odd functions), and Gauss-Radau quadrature formula with Chebyshev weight function , based on n+1 nodes, holds exactly for polynomical function x2n+2.