Fourier-Jacobi级数的Vallee-Poussin和逼近

The Approximation of continuous Functions by vallee-Poussin Sums of Fourier-Jacobi Series

该文研究了连续函数的Fourier-Jacobi级数的Vallee-Poussin和逼近问题,主要得到 |σ_n^(α,β)(f,x)|≤cE_n(f)(-1<α,β≤-1/2)这样附带地改进了近来刘瑞珍得到的关于Fourier-Tchebycheff级数的Vallee-Poussin和逼近的结果。

The approximation of continuous function f(x) on theinterval [-1, 1] by Vallee--Poussin sums σ_n^(α,β)(f,x) of Fourier-Jacobiseries is considered. It's mainly showed that for. -1<α, β≤-1/2 |σ_n^(α,β) (f,x)-f(x)|≤cE_n(f)therefore a main result obtained by Liu Ruizhen is improved, whereE_n(f) is the n-order best approximation of f.