论文标题
在Legendre近似方面的改进
An improved bound on Legendre approximation
论文作者
论文摘要
在本文中，获得了Legendre多项式的衍生物之间的新关系，并且通过这些关系，提供了可区分功能的Legendre系数的新上限。这些上限是锋利的，涵盖了更多可区分功能的类别。此外，提供了Legendre多项式部分总和的近似值的新范围。给出数值示例以验证我们的理论结果。
In this paper, new relations between the derivatives of the Legendre polynomials are obtained, and by these relations, new upper bounds for the Legendre coefficients of differentiable functions are presented. These upper bounds are sharp and cover more categories of differentiable functions. Moreover, new and sharper bounds for the approximation error of the partial sums of Legendre polynomials are provided. Numerical examples are given to validate our theoretical results.
