Asymptotic behavior of intermediate points in the differential mean value theorem of divided differences with repetitions

作者：Xu, Aimin^*; Cui, Feng; Hu, Zhicheng

来源：Journal of Mathematical Analysis and Applications, 2010, 365(1): 358-362.

DOI：10.1016/j.jmaa.2009.10.067

• Asymptotic behavior
• Bell polynomial
• Cycle index of symmetric group
• Divided difference
• Mean value theorem

By the explicit representation for the divided differences with repetitions involving cycle index of symmetric groups, this paper deals with the asymptotic behavior of the intermediate point of the mean value theorem of divided differences with repetitions. Our results generalize some recent interesting results such as the asymptotic expansions of the immediate points of the Taylor formula and the differential mean value theorem of divided differences with distinct points.

• 出版日期2010-5-1
• 单位浙江万里学院; 浙江工商大学; 浙江大学