【摘要】 泰勒公式中ξ位置的确定黄炳生（东南大学数学力学系，南京２１００１８）美国数学月刊［１］给出了ｘ在确定情况下，求得计算函数ｆ（ｘ）的泰勒公式中的ξ的近似值的方法，但对此近似值是否收敛于ξ并未证明，且对ｘ作为；的函数ξ（ｘ）的各阶导数的存在性亦未给以明确...更多还原

【Abstract】 This paper proved that the intermediate value ξ in Taylor’s equation is a continuously dif-ferentiable function ξ(x), and found the ξ(n)(x0), n=1 , 2 , 3 , …, so that ξ have Taylor expansion.It is proved that also the remainder term in Taylor’s equation tends to zero, so that the expansion of ξin a Taylor series is available, at last expansion of ξ for function sin is provided.更多还原