Divided Differences of Implicit Functions

Abstract

Under general conditions, the equation $g(x,y)=0$ implicitly defines $y$ locally as a function of $x$. In this article, we express divided differences of $y$ in terms of bivariate divided differences of $g$, generalizing a recent result on divided differences of inverse functions.

References in corpus (1)

• Implicit higher derivatives, and a formula of Comtet and Fiolet

Cited by in corpus (1)

• Divided Differences of Multivariate Implicit Functions