基于对称偏导数的多元函数Taylor公式及可微性分析

Study of Taylor Formula and Differentiability for Multivariate Function based on the Symmetric Partial Derivative

引入多元函数对称偏导和对称可微的定义,讨论多元函数在对称偏导数意义下的Taylor公式及多元函数对称可微的充分条件和必要条件.

First, the definition of the symmetric partial derivative and the symmetric differentiability of multivariate function are introduced in this paper. Second, the Taylor formula for multivariate function based on the symmetric partial derivative is given. Finally, the sufficient condition and the necessary condition for the symmetric differentiability of multivariate function are obtained.