In this paper, we study the Jacobi frame approximation with equispaced samples and derive an error estimation. We observe numerically that the approximation accuracy gradually decreases as the extended domain parameter $\gamma$ increases in the uniform norm, especially for differentiable functions. In addition, we show that when the indexes of Jacobi polynomials $\alpha$ and $\beta$ are larger (for example $\max\{\alpha,\beta\} > 10$), it leads to a divergence behavior on the frame approximation error decay.

翻译：在本文中,我们研究雅各比框架的近似值,并得出一个错误估计。我们从数字上观察到,随着扩展域参数($\gamma$)在统一规范中,特别是对于不同功能,随着扩展域参数($\gamma$)的增加,近地近地精度逐渐下降。此外,我们显示,当雅各比多民族指数($\alpha$和$\beta$)的指数较大(例如$\max ⁇ alpha,\beta ⁇ > 10美元)时,它会导致框架近地误差衰减的偏差行为。