Darboux’s formula with integral remainder of functions with two independent variables

摘要

In the article, the well-known Darboux’s formula of functions with single variable is generalized to that of functions of two independent variables with integral remainder, some important special cases of Darboux’s formula of functions with two variables are obtained, and some estimates of the integral remainders and Darboux’s expansion of the function ln(x + y) are given. These results generalize Sard’s formula in numerical integration.