一类广义Gauss型求积公式  

Generalized Gaussian Quadrature Formulas

作　　者：曹丽华[1] 

机构地区：[1]深圳大学数学与计算科学学院数学系,深圳518060

出　　处：《数学物理学报（A辑）》2007年第3期524-534,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(10571121);广东省自然科学基金(5010509)资助

摘　　要：基于被积函数在n次第一类和第二类Chebyshev多项式的零点处的差商,该本构造了两种Gauss型求积公式,这些求积公式包含了某些已知结果作为特例。更重要的是这些新结果与Gauss-Turán求积公式有密切的联系。The purpose of this paper is to construct a generalized Gaussian quadrature rule based on the divided differences of the integrand at the zeros of the n-th Chebyshev polynomial of the first kind. Another similar quadrature rule based on the divided differences at the zeros of the n-th Chebyshev polynomial of the second kind is also considered. The obtained results include some existing results as special cases. The interesting thing here is that these new results are closely related to the so-called Gauss-Turán quadrature formulas.

关 键 词：广义Gauss型求积公式 Gauss-Turán求积公式 s-正交多项式 Cotes数 最高代数精度 

分 类 号：O174.41[理学—数学]