| 高阶微分中值定理 |
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| 引用本文： | 匡继昌. 高阶微分中值定理[J]. 北京教育学院学报(自然科学版), 2014, 0(3): 1-5 |
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| 作者姓名： | 匡继昌 |
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| 作者单位： | 湖南师范大学数学与计算机科学学院,长沙,410081 |
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| 基金项目： | 国家自然科学基金项目;项目 |
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| 摘 要： | 将"微积分"教学中的微分中值定理推广到高阶导数,从而可由此直接推出Taylor公式.对于推广后的高阶微分中值定理,给出了一个简单明了的新证明.也考虑到了开区间和单侧导数等情形.
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| 关 键 词： | 中值定理 高阶微分 Taylor公式 |
Higher Order Differentiation Mean Value Theorem |
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| Kuang Jichang. Higher Order Differentiation Mean Value Theorem[J]. Journal of Beijing Institute of Education(Natural Science Edition), 2014, 0(3): 1-5 |
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| Authors: | Kuang Jichang |
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| Affiliation: | Kuang Jichang(Department of Mathematics,Hunan Normal University, Changsha Hunan 410081,China) |
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| Abstract: | The aim of this paper is to generalize the classical mean value theorem to the higher orderdifferentiation. A simple proof of the higher order differentiation mean value theorem is given. As a spe-cial case, a new proof of Taylor’s formula is also given. On the open interval and one-sided derivativesare considered. |
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| Keywords: | mean value theorem higher order differentiation Taylor formulation |
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