反正切函数的Hermite插值型多项式逼近  

Hermite interpolating-like polynomials for approximating arctangent

作　　者：孟令雄[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,湖南长沙410081

出　　处：《湖南文理学院学报（自然科学版）》2010年第4期1-2,共2页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：国家自然科学基金(10571078);湖南师范大学青年基金资助

摘　　要：从简单有理函数{[x4m(1-x)4m]/[1+x2]}出发构造了一列一致收敛到arctanx的多项式,这列多项式不仅收敛速度比Taylor级数快,而且在每个点处收敛速度很快.另外发现这列多项式还具有Hermite插值多项式的性质.Arising from a simple family of rational functions {[x4m（1-x）4m]/[1＋x2]},a sequence of polynomials that convergences the function arctan x uniformly on [0,1] is constructed.This sequence not only approximates so much more rapidly than the normal one of Taylor polynomials centered at 0,but also its rate of convergence at any points on [0,1] is very rapid.Moreover,it is shown that this polynomials have the property of Hermite-interpolating polynomials.

关 键 词：HERMITE插值 arctanx 一致收敛 

分 类 号：O174.42[理学—数学]