High Order Difference Quotient Formulas of Multivariate Functions

To promote the main results of function approximation theory to the multivariate function, the following work was presented in this paper by some skills of combination formula:the unified expression of the high order difference quotient formulas of multivariate function was established; the difference formula of the high order directional derivative was proven; the approximate high order partial derivative was studied; and the second-order partial derivative of the multivariate function and the truncation errors of the center difference quotient of the Hessian matrix were given.