摘要
本文研究了基于Jacobi多项式J_n^((α,β))(x)(0<α,β<1)的零点{x_k}_1~n的Grnwald插值多项式G_n(f;x)=sum from k=1 to n (f(x_k)l_k^2(x)),证明了G_n(f;x)在(-1,1)内的任一闭子区间上一致收敛于连续函数f(x);从而拓广了Grnwald所得结果。
In this paper, Grunwald interpolatory polynomials Gn(f; x) =sum from k=1 to n(f(xk)lk2(x))based on the zeros of Jacobi polynomials Jn(α,β(x) (0<<<<<a,β<l) are studied, it has proved that Gn(f;x) converges uniformly continuous f(x) on any 〔a,b〕(?) (-1,1), extended the results of G. Grunwald〔1〕.
