具扩充Jacobi结点的Lagrange插值逼近

Jacobi Expansion with Lagrange Interpolation Nodes

研究以扩充Jacobi多项式(1+x)Vn(x)的零点{xk}kn=0为基点的Lagrange插值多项式Ln(f,x)同时逼近f(x)的问题,得到相关的逼近的阶的估计以及导数逼近的估计.

Let V,,（x） be Jaeobi polynomial with n order, Ln（f,x） be the Lagrange interpolation based on the zeros of polynomial （ 1 ＋ x） Vn （x）. In this paper, we studied the problems of the simultaneous approximation of a function and its derivative by Lagrange interpolation polynomial. Be related to the estimated order of approximation and the approximation of the estimated derivative.